Lesson: Simplifying Roots

Comment on Simplifying Roots

as X = √25
X can be equal to + or - 5?
as squaring both positive and negative 5 produces the same result 25
greenlight-admin's picture

25 has two square roots (5 and -5). However, the √ NOTATION tells us to take only the positive root. So, √25 = 5

So the square root of bx^2 is bx, is that correct?
greenlight-admin's picture

It depends on whether you are squaring both b and x.

In general, √(something²) = something

For example, √(7²) = 7 and √(183²) = 183

So, √(bx)² = bx

However, √(bx²) = (√b)(x). Here's why:

We know that √(xy) = (√x)(√y)

So, √(bx²) = (√b)[√(x²)] = (√b)[x]

Does that help?

https://greprepclub.com/forum/x-and-y-are-positive-integers-2537.html
I do not understand the solution to this question
greenlight-admin's picture

Here's another approach: https://greprepclub.com/forum/x-and-y-are-positive-integers-2537.html#p3...

Does that help?

Cheers,
Brent

Hi Brent,

You did add the numbers in this (https://greprepclub.com/forum/compute-the-value-9068.html)question. But here https://www.greenlighttestprep.com/module/gre-powers-and-roots/video/1042 the rule says against doing so.

I am unable to understand. Could you please help me out.
Thanks,
Ketan
greenlight-admin's picture

In this question (https://greprepclub.com/forum/compute-the-value-9068.html), we must evaluate √(81 + 9)
So, we can first simplify the part in brackets to get √90 (which is what I did in my solution)

At 2:46 in my video lesson (https://www.greenlighttestprep.com/module/gre-powers-and-roots/video/1042), I say that √(a + b) does NOT equal √a + √b

In other words, √(81 + 9) does NOT equal √81 + √9
So, my solution (at https://greprepclub.com/forum/compute-the-value-9068.html) does not break any rules.

Does that help?

Cheers,
Brent

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