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29 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Even exponents hide the sign of the original number, because they always result in a positive number. True or false? |
True. If x^4 = 16 then X could be either -2 or +2. Similarly, in x^2 = 16 , value of X could be -4 or +4. You can use both negative and positive answers where the variable is squared and you're taking the root yourself. If the root is already given on GMAT, use only positive value/answer. |
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Odd roots always have one solution. True or false |
True. Odd roots keep the sign of the base as it is. So it could be positive or negative, depending on the sign of the value for which odd root is being taken. Example: 3√(-27) = -3 |
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True |
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On the GMAT, the square roots will have only positive answer. That is if an even square root appears on question, or in your solution, use only positive value. |
True. Example |
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For all positive numbers, the square root preserves the order of inequality. True or False? |
True. In other words, if A < B < C, then √A < √B < √C. |
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√2 = ? |
1.4 |
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√3 = ? |
1.7 |
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√5 = ? |
2.2 |
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Regardless of Y is positive or negative, √(y)^2 = | y | |
True. |
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A number is a perfect square if the unit digit of that big number is a perfect square. |
For example, 9604 is a perfect square because it has 4 as it's unit digit. Similarly, 7569 and 2916. |
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The perfect squares other than 0 and 1 are those numbers whose prime factors have even exponents |
For example, 49 is a perfect square and 7x7 is it's prime factors which are ultimately 7^2 i.e. it's prime factor 7 has an even exponent. In another example, 100 is 10^2 or 5^2 X 2^2. |
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In general, if n is even then n√(x)^n = |x| and if n is odd then n√(x)^n = x |
True. |
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A perfect square other than 0 and 1 is a number whose prime factorization consists of only even exponents. |
For example. 25 is a perfect square which is 5^2. However 24 is not a perfect square because it's prime factors consists of 2^3 x 3 |
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A positive perfect cube root, other than 1, is a number whose prime factorization consists only exponents that are multiple of 3 |
True. For example in 279 whose prime factorization is 9^3 consists of exponent 3 which is a multiple of 3. |
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Even index in a root cancel out the sign of the number under them and are always positive. |
True. For example square or fourth roots always result in positive numbers i.e the square root of a negative number is not a real number. |
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Memorize |
√2 = 1.4 √3 = 1.7 √5 = 2.2 √6 = 2.4 √7 = 2.6 √8 = 2.8 √11 = 3.3 |
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On the GMAT , if the denominator of a fraction consists of a radical, it's not the simplest form and we must remove the radical by rationalization. |
True. For example 3/√5 is not in it's simplest form and acceptable, we must make it 3(√5)/5 by rationalizing i.e. multiplying the numerator and denominator by √5. |
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When x = √144 then the answer would be 12 because gmat wants to only consider positive root. However √(x^ 2) = √144 will be will x = +-12 |
This is because √x^2 is equal to |x| where x could be positive or negative as |x| is just a distance from number line from both positive and negative ways. |
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We must ALWAYS check answers gotten by equations involving square roots to see if they solve the equation |
Some roots are externous roots and don't solve or satisfy the equations involving square roots. |
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If bases are equal then exponents will also be equal. This will not be true only when the base is -1, 0, and 1. |
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Numbers in Roots can be compared to see which is larger or smaller by taking first LCM of all denominators of fraction exponents and raising these numbers with this LCM. |
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Numbers which are represented in exponents can be compared by taking GCF of the exponents themselves and then raising the exponents of the numbers to the reciprocal of the GCF. |
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True. Exponent with negative powers can be inverted to get positive powers. |
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Positive integers having even number of zeroes to the right of first non zero digit are perfect squares. Such perfect squares have half the trailing zeroes in their square roots. |
Example,10000 is a perfect square whose square root has only two zeroes that is 100.
Similarly, 40,000 is a perfect square with a square root of the 200. |
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A perfect square and it's square root in case of decimals will always have a finite number of decimals. |
True. Example 0.16 is a perfect square with square root of 0.4. |
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A perfect square's square root in case of decimals will always have exactly half the number of decimals places as it's perfect square. This also means the decimal that is a perfect square will always have even number of decimals places. |
True. 0.0004 is a perfect square and it's square root √0.0004 is 0.02 that is it has now half the decimals places. |
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The cube root of a perfect cube will have exactly one third number of zeroes to the right of the final non zero digit as the original perfect cube. |
True. Cube root of 1,000,000 is 100 while that of 27,000 is 30 |
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The cube root of a perfect cube fraction / decimal will have exactly one third number of decimals places as the original perfect cube. |
True. 0.000027 has a cube root of 0.03. |
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An integer with zeroes in it's digit will be a cube root only if these number of zeroes is a multiple of three since it's cube root can only have one third of zeroes hence it the number of zeroes has to be a multiple of 3.
Similarly, the number of decimals places in a cube root which has fraction / decimals has to be a multiple of 3. |
True.
1,000,000 is a cube root because it's zeroes are 6 which is a multiple of 3 hence it's cube root is 100.
Similarly, 0.000027 is a perfect cube because total decimals places are 6 hence it's cube root will be 0.03 |
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