Square root

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Stockmoose16: Master | Next Rank: 500 Posts; Posts: 347; Joined: Mon Aug 04, 2008 1:42 pm; Thanked: 1 times

by Stockmoose16 » Mon Aug 04, 2008 3:32 pm

This is a question from MGMAT book:

Find the square root of 72

They simplify the square root down to the prime numbers, making it the sq. rt of 3*3*2*2*2. Combining factors: you get the sq root of 9 * sq rt of 4 * sq 2. The answer is then: 3 *2 * sq rt 2 = 6 sq rt 2

I did it a different way, and got a different answer. Is this correct or incorrect:

Sq rt of 72 = sq rt of 9 * sq rt of 8 = 3 sq rt of 8

Is this right?

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Source: Beat The GMAT — Problem Solving | Mon Aug 04, 2008 3:32 pm

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Re: Square root

by Ian Stewart » Mon Aug 04, 2008 3:41 pm

Stockmoose16 wrote:This is a question from MGMAT book:

Find the square root of 72

They simplify the square root down to the prime numbers, making it the sq. rt of 3*3*2*2*2. Combining factors: you get the sq root of 9 * sq rt of 4 * sq 2. The answer is then: 3 *2 * sq rt 2 = 6 sq rt 2

I did it a different way, and got a different answer. Is this correct or incorrect:

Sq rt of 72 = sq rt of 9 * sq rt of 8 = 3 sq rt of 8

Is this right?

It is correct- root(72) and 3root(8) are equal. But, 3root(8) is not completely simplified. Whenever you can divide what's under the root by a perfect square larger than 1, you need to factor that perfect square out. We can divide 8 by 4 = 2^2, so we need to divide 4 out:

3root(8) = 3root(4*2) = 3*root(4)*root(2) = 3*2*root(2) = 6*root(2)

You should be able to do that in one step (not five) with practice.

This is much like reducing fractions in that you need to do it, because otherwise your answer won't look like any of the five answer choices on the test.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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