Simplify the square root of 45.?

Question

I got 6.71 is this right?

Answer 1

That's what you get if you evaluate sqrt(45) and round to the nearest hundredth. However, simplifying a square root does not usually refer to evaluating, but rather to bringing square factors out of the radical. You can rewrite sqrt(45) as sqrt(9)*sqrt(5), because the square root is really the same as raising to the power of 1/2, and an exponent can be distributed across multiplication. Since sqrt(9) = 3, you can simplify sqrt(45) into 3*sqrt(5).

Answer 2

square root 45 45 = 9*5 45 = 3 sqrt(5)

Answer 3

Square root of 45 is equal to square root of 9 x square root of 5, and is equal to:

= sqrt 9 x sqrt 5
= 3 x sqrt 5

That's the simplest we could go without going to a square root table or using a calculator. Note that I used sqrt in place of a radicand symbol not available in my computer.

Answer 4

The answer 6.71 is only an approximation, as is any decimal representation of an irrational number. In math class, they want the EXACT answer. Simplifying a square root means pulling everything out from under the radical that you can, leaving anything under the radical sign that cannot be expressed exactly as a ratio of two integers.

In the case of the square root of 45:

45 can be factored as 3^2 * 5. You can pull prime factors out from under the radical sign in matching pairs, in this case, the two 3's. When the matching pair is pulled out from under the radical sign, only one of the pair comes out, in this case, one of the 3's. The 5 has to stay under the radical sign, so the answer is

sqrt (45)
= sqrt (3*3*5)
= sqrt (3*3) * sqrt (5)
= 3 * sqrt (5)

Answer 5

the square root of 45 is the same as the square root of (9 times 5) this can be applied to any square roots, split it up between it's multiples if you know one or any of the multiples is an easy root to find.
So now you know square root of 9 is 3, and since square root of 5 has no simple way of writing it, you get the simple version of square root 45 is 3 times the square root of 5

Answer 6

"Simplifying" usually means either solving the root exactly, or leaving a smaller root with a coefficient. In this case, the answer is:

sqrt(45) = sqrt(9 * 5) = 3 * sqrt(5)

Answer 7

The exact answer is given by:-
√45 = √(9 x 5) = 3√5

If you wish , an approximate answer would then be 3 x 2.24 = 6.72

Answer 8

sqrt(45) = sqrt(9) * sqrt(5) = 3 * sqrt(5)

Answer 9

sqrt(45)=3sqrt(5)=6.708