Simplifying Square Roots
The problem requires simplifying and adding two square roots: $\sqrt{75}$ and $\sqrt{147}$.
Step 1: Simplify $\sqrt{75}$
Find the largest perfect square that divides 75. This is 25, since $75 = 25 \times 3$. Therefore:
$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$
Step 2: Simplify $\sqrt{147}$
Find the largest perfect square that divides 147. This is 49, since $147 = 49 \times 3$. Therefore:
$\sqrt{147} = \sqrt{49 \times 3} = \sqrt{49} \times \sqrt{3} = 7\sqrt{3}$
Step 3: Add the Simplified Roots
Now add the results from Step 1 and Step 2:
$5\sqrt{3} + 7\sqrt{3}$
Since both terms have the same radical part ($\sqrt{3}$), we can add their coefficients:
$(5 + 7)\sqrt{3} = 12\sqrt{3}$
Final Value Calculation
The value of $\sqrt{75} + \sqrt{147}$ is $12\sqrt{3}$. This corresponds to Option 4.
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Important Questions from Surds and Indices
Find the cube root of 78402752
Find the value of :
[(3 × 3 × 3 × 3 × 3 × 3) 6 ÷ (3 × 3 × 3 × 3) 7 × 3 4]
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
