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

Algebra ->  Radicals -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do A and C to help you get started


A)



sqrt%2845%29 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


sqrt%289%2A5%29 Factor 45 into 9*5

sqrt%289%29%2Asqrt%285%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

3%2Asqrt%285%29 Take the square root of the perfect square 9 to get 3

So the expression sqrt%2845%29 simplifies to 3%2Asqrt%285%29

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

sqrt%2845%29=6.70820393249937

and if we evaluate 3%2Asqrt%285%29 we get

3%2Asqrt%285%29=6.70820393249937

This shows that sqrt%2845%29=3%2Asqrt%285%29. So this verifies our answer







C)



sqrt%2816%2F25%29 Start with the given expression


sqrt%2816%29%2Fsqrt%2825%29 Break up the square root



%284%29%2Fsqrt%2825%29 Simplify sqrt%2816%29 to get 4 (note: If you need help with simplifying square roots, check out this solver)


%284%29%2F%285%29 Simplify sqrt%2825%29 to get 5



So sqrt%2816%2F25%29=4%2F5