Simplify: sqrt(50) − 3sqrt(3)(sqrt(2) − 5) − 5sqrt(32)

Question

ScanSolve AI Tutor · Accepted Answer

To solve the expression, we will simplify each radical term and then combine like terms.

The expression is:

\sqrt{150} - 3\sqrt{3}(2\sqrt{2} - 5) - 5\sqrt{32}

Simplify each square root.
$\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}$ $\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$
Distribute the term $3\sqrt{3}$ into the parentheses $(2\sqrt{2} - 5)$ .
$3\sqrt{3}(2\sqrt{2} - 5) = (3\sqrt{3} \times 2\sqrt{2}) - (3\sqrt{3} \times 5)$ $= (3 \times 2 \times \sqrt{3 \times 2}) - (3 \times 5 \times \sqrt{3})$ $= 6\sqrt{6} - 15\sqrt{3}$
Substitute the simplified terms back into the original expression.
$5\sqrt{6} - (6\sqrt{6} - 15\sqrt{3}) - 5(4\sqrt{2})$
Remove the parentheses and simplify the last term.
$5\sqrt{6} - 6\sqrt{6} + 15\sqrt{3} - 20\sqrt{2}$
Combine like terms.
$(5\sqrt{6} - 6\sqrt{6}) + 15\sqrt{3} - 20\sqrt{2}$ $-\sqrt{6} + 15\sqrt{3} - 20\sqrt{2}$
The terms are all unlike, so they cannot be combined further.

Simplify: sqrt(50) - 3sqrt(3)(sqrt(2) - 5) - 5sqrt(32)