Question
What value of \( x \) will make the equation true? \( (\sqrt{5})(\sqrt{5})=x \)
Ask by Greene Erickson. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 5 \)
Solution
To solve the equation:
\[
\sqrt{5} \times \sqrt{5} = x
\]
**Step 1: Understand the Multiplication of Square Roots**
When you multiply two square roots of the same number, the operation simplifies to the number itself. Mathematically, this is expressed as:
\[
\sqrt{a} \times \sqrt{a} = a
\]
**Step 2: Apply This to the Given Equation**
Applying this property to your equation:
\[
\sqrt{5} \times \sqrt{5} = 5
\]
**Conclusion**
So, the value of \( x \) that makes the equation true is:
\[
x = 5
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the value of \( x \) that makes the equation true, we can simplify the left side: \( (\sqrt{5})(\sqrt{5}) \) is equal to \( 5 \). Therefore, \( x = 5 \) makes the equation correct! Another fun little twist here is that the square root has its own magical properties! When you multiply the square root of a number by itself, you’re essentially "undoing" the square root operation, hence arriving back at the original number. So, in this case, the mystery of \( x \) has been solved: it’s just 5!
