Question

\( (20)^2 - \sqrt{324} = \)

• A. 400
• B. 18
• C. 382
• D. 328

Hint:

Remember common squares and square roots to speed up calculations. For larger numbers, try prime factorization or estimation.

Answer 1

The Correct Option is C

Step 1: Calculate the square of 20.
$$ (20)^2 = 20 \times 20 = 400 $$ Step 2: Calculate the square root of 324.
We need to find a number that, when multiplied by itself, equals 324. We can try to estimate or factorize 324.
Notice that \( 10^2 = 100 \) and \( 20^2 = 400 \), so the square root should be between 10 and 20.
The number ends in 4, so its square root should end in either 2 or 8. Lets try 18: \( 18 \times 18 \):
\( 8 \times 8 = 64 \) (ends in 4, carry 6)
\( 8 \times 1 = 8 + 6 = 14 \)
\( 1 \times 8 = 8 \)
\( 1 \times 1 = 1 \)
Adding these: \( 140 + 80 + 4 = 324 \)
So, \( \sqrt{324} = 18 \)
Step 3: Substitute the calculated values back into the expression.
$$ (20)^2 - \sqrt{324} = 400 - 18 $$ Step 4: Perform the subtraction.
$$ 400 - 18 = 382 $$ Therefore, \( (20)^2 - \sqrt{324} = 382 \).