SOLUTION: write √45 in the form k√5, where k is an integer

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Question 288382: write √45 in the form k√5, where k is an integer
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Simplifying Square Roots (whole numbers only)
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




Since sqrt%2845%29=3%2Asqrt%285%29, this means that k=3