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

Question 288382: write √45 in the form k√5, where k is an integer
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Simplifying Square Roots (whole numbers only)

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

Since , this means that

SOLUTION: write &#8730;45 in the form k&#8730;5, where k is an integer

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