Evaluate 5 square root of 24-8 square root of 150

$5 \sqrt{24} - 8 \sqrt{150}$

Step 1

Simplify each term.

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$5 \sqrt{4 (6)} - 8 \sqrt{150}$

Rewrite $4$ as $2^{2}$ .

$5 \sqrt{2^{2} \cdot 6} - 8 \sqrt{150}$

$5 \sqrt{2^{2} \cdot 6} - 8 \sqrt{150}$

Pull terms out from under the radical.

$5 (2 \sqrt{6}) - 8 \sqrt{150}$

Multiply $2$ by $5$ .

$10 \sqrt{6} - 8 \sqrt{150}$

Rewrite $150$ as $5^{2} \cdot 6$ .

Factor $25$ out of $150$ .

$10 \sqrt{6} - 8 \sqrt{25 (6)}$

Rewrite $25$ as $5^{2}$ .

$10 \sqrt{6} - 8 \sqrt{5^{2} \cdot 6}$

$10 \sqrt{6} - 8 \sqrt{5^{2} \cdot 6}$

Pull terms out from under the radical.

$10 \sqrt{6} - 8 (5 \sqrt{6})$

Multiply $5$ by $- 8$ .

$10 \sqrt{6} - 40 \sqrt{6}$

$10 \sqrt{6} - 40 \sqrt{6}$

Step 2

Subtract $40 \sqrt{6}$ from $10 \sqrt{6}$ .

$- 30 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 30 \sqrt{6}$

Decimal Form:

$- 73.48469228 \dots$

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