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

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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

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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

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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