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Chapter 8: Problem 63

Simplify. All variables represent positive values. $$4 \sqrt{63}+6 \sqrt{112}$$

Short Answer

Expert verified
The simplified form of the given expression is \(36 \sqrt{7}\).

Step by step solution

01

Simplify the first square root term

In the term \(4 \sqrt{63}\), 63 is the number beneath the square root. To simplify this, look for perfect square factors of 63. The largest perfect square factor of 63 is 9. So, rewrite 63 as \(9*7\), and the term as \(4 \sqrt{9 * 7}\).
02

Perform the square root operation on the first term

Now, perform the square root operation for 9 which gives us 3 and the first term simplifies as \(4 * 3 \sqrt{7}\) which is \(12 \sqrt{7}\).
03

Simplify the second square root term

In the term \(6 \sqrt{112}\), 112 is the number underneath the square root. Similarly, look for perfect square factors of 112. The largest perfect square factor of 112 is 16. So, rewrite 112 as \(16*7\), and the term as \(6 \sqrt{16 * 7}\).
04

Perform the square root operation on the second term

Now, perform the square root operation for 16 which gives us 4 and the second term simplifies as \(6 * 4 \sqrt{7}\) which is \(24 \sqrt{7}\).
05

Add the simplified terms

Finally, add the simplified terms \(12 \sqrt{7}\) and \(24 \sqrt{7}\) to get \(36 \sqrt{7}\).

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Most popular questions from this chapter

Rationalize the numerator of \(\frac{\sqrt{5}+2}{5}\).

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