How to simplify square roots - GRE Quantitative Reasoning

easiest way to simplify: turn into scientific notation

√0.0000490= √4.9 X 10-5

finding the square root of an even exponent is easy, and 49 is a perfect square, so we can write out an improper scientific notation:

√4.9 X 10-5 = √49 X 10-6

√49 = 7; √10-6 = 10-3 this is equivalent to raising 10-6 to the 1/2 power, in which case all that needs to be done is multiply the two exponents: 7 X 10-3= 0.007

First find all of the prime factors of

So

√75 can be broken down to √25 * √3. Which simplifies to 5√3.

In order to take the square root, divide 576 by 2.

Rewrite what is under the radical in terms of perfect squares:

Therefore, .

Multiply by the conjugate and the use the formula for the difference of two squares:

We know that 25 is a factor of 50. The square root of 25 is 5. That leaves which can not be simplified further.

1. We know that , which we can separate under the square root:

2. 144 can be taken out since it is a perfect square: . This leaves us with:

This cannot be simplified any further.

You can rewrite the equation as .

This simplifies to .

Begin by multiplying top and bottom by √(3):

(√(18) + √(9)) / 3

Note the following:

√(9) = 3

√(18) = √(9 * 2) = √(9) * √(2) = 3 * √(2)

Therefore, the numerator is: 3 * √(2) + 3. Factor out the common 3: 3 * (√(2) + 1)

Rewrite the whole fraction:

(3 * (√(2) + 1)) / 3

Simplfy by dividing cancelling the 3 common to numerator and denominator: √(2) + 1

easiest way to simplify: turn into scientific notation

√0.0000490= √4.9 X 10-5

finding the square root of an even exponent is easy, and 49 is a perfect square, so we can write out an improper scientific notation:

√4.9 X 10-5 = √49 X 10-6

√49 = 7; √10-6 = 10-3 this is equivalent to raising 10-6 to the 1/2 power, in which case all that needs to be done is multiply the two exponents: 7 X 10-3= 0.007

First find all of the prime factors of

So

√75 can be broken down to √25 * √3. Which simplifies to 5√3.

In order to take the square root, divide 576 by 2.

Rewrite what is under the radical in terms of perfect squares:

Therefore, .

Multiply by the conjugate and the use the formula for the difference of two squares:

We know that 25 is a factor of 50. The square root of 25 is 5. That leaves which can not be simplified further.