SOLUTION: simplify the expression a)square root of 45 b)square root of 54 c)square root of 16/25 d)square root of 10/32

Question 120559: simplify the expression
a)square root of 45
b)square root of 54
c)square root of 16/25
d)square root of 10/32
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do A and C to help you get started

A)

Start with the given expression

The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.

So let's list the factors of 45

Factors:
1, 3, 5, 9, 15, 45

Notice how 9 is the largest perfect square, so lets factor 45 into 9*5

Factor 45 into 9*5

Break up the square roots using the identity

Take the square root of the perfect square 9 to get 3

So the expression simplifies to

----------------------------
Check:
Notice if we evaluate the square root of 45 with a calculator we get

and if we evaluate we get

This shows that . So this verifies our answer

C)

Start with the given expression

Break up the square root

Simplify to get (note: If you need help with simplifying square roots, check out this solver)

Simplify to get

So

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