Question

Find ? in equation: ?/\(\sqrt{128}\) = \(\sqrt{162}\)/?

• A. 12
• B. 14
• C. 144
• D. 196

Hint:

Always try to simplify square roots by factoring out perfect squares before performing multiplication. This often makes the calculation much easier and reduces the chance of errors. For example, $\sqrt{128} = \sqrt{64 \times 2}$ rather than directly multiplying large numbers.

Answer 1

The Correct Option is C

Step 1: Cross multiply the equation.
Let the unknown be \( x \). The equation \( \frac{x}{\sqrt{128}} = \frac{\sqrt{162}}{x} \) cross multiplies to \[ x^2 = \sqrt{128} \times \sqrt{162} \]

Step 2: Combine the two square roots into one before simplifying.
Using \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \), we get \[ x^2 = \sqrt{128 \times 162} = \sqrt{20736} \]

Step 3: Take the square root and solve for x.
Since \( 144 \times 144 = 20736 \), we get \( \sqrt{20736} = 144 \), so \( x^2 = 144 \), and taking the square root of both sides gives \[ \boxed{x = 12} \]