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13:59 5G 804 siyavula.com Siy \( 2 \sqrt{u} 12 \) (i) You have a new assignment CLOSE due on 31 Oct, 13:00: YEAR END EXAM. Go to My Assignments Choose a language Algebraic expressions (Part 1): Simplifying SQUARE \& CUBE ROOTS Simplify (evaluate) the following expression: \[ (\sqrt{k})^{2} \] Answer: Check answer 2 attempts remaining Help! How should I type my answer? Share this question

Ask by Blake Gibbs. in South Africa
Feb 08,2025

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Tutor-Verified Answer

Answer

The simplified expression is \( k \).

Solution

The expression is (√k)². Squaring a square root cancels the square root, which means you get back the original number under the square root, assuming k is nonnegative. Mathematically:   (√k)² = k So the simplified expression is k.

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Beyond the Answer

When you simplify \((\sqrt{k})^{2}\), you're essentially using the property of square roots where squaring and taking the square root are inverse operations. So, \((\sqrt{k})^{2} = k\). It’s like peeling an orange; once you remove the skin, you get to the juicy fruit inside—no need to keep the skin around! To dive a bit deeper, remember that square roots can only be simplified when dealing with non-negative numbers. So, if \(k\) is positive or even zero, you’re all set! However, if \(k\) were negative, you’d venture into complex numbers territory. This can make your math even more interesting—just like adding a little spice to your favorite dish!

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