Simplify 3 square root of 20(2 square root of 5-7)

$3 \sqrt{20} (2 \sqrt{5} - 7)$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$3 \sqrt{4 (5)} (2 \sqrt{5} - 7)$

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

$3 \sqrt{2^{2} \cdot 5} (2 \sqrt{5} - 7)$

Pull terms out from under the radical.

$3 (2 \sqrt{5}) (2 \sqrt{5} - 7)$

Multiply $2$ by $3$ .

$6 \sqrt{5} (2 \sqrt{5} - 7)$

Apply the distributive property.

$6 \sqrt{5} (2 \sqrt{5}) + 6 \sqrt{5} \cdot - 7$

Multiply $6 \sqrt{5} (2 \sqrt{5})$ .

Multiply $2$ by $6$ .

$12 \sqrt{5} \sqrt{5} + 6 \sqrt{5} \cdot - 7$

Raise $\sqrt{5}$ to the power of $1$ .

$12 ({\sqrt{5}}^{1} \sqrt{5}) + 6 \sqrt{5} \cdot - 7$

Raise $\sqrt{5}$ to the power of $1$ .

$12 ({\sqrt{5}}^{1} {\sqrt{5}}^{1}) + 6 \sqrt{5} \cdot - 7$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 {\sqrt{5}}^{1 + 1} + 6 \sqrt{5} \cdot - 7$

Add $1$ and $1$ .

$12 {\sqrt{5}}^{2} + 6 \sqrt{5} \cdot - 7$

Multiply $- 7$ by $6$ .

$12 {\sqrt{5}}^{2} - 42 \sqrt{5}$

Simplify each term.

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$12 {(5^{\frac{1}{2}})}^{2} - 42 \sqrt{5}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$12 \cdot 5^{\frac{1}{2} \cdot 2} - 42 \sqrt{5}$

Combine $\frac{1}{2}$ and $2$ .

$12 \cdot 5^{\frac{2}{2}} - 42 \sqrt{5}$

Cancel the common factor of $2$ .

Cancel the common factor.

$12 \cdot 5^{\frac{2}{2}} - 42 \sqrt{5}$

Rewrite the expression.

$12 \cdot 5^{1} - 42 \sqrt{5}$

Evaluate the exponent.

$12 \cdot 5 - 42 \sqrt{5}$

Multiply $12$ by $5$ .

$60 - 42 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$60 - 42 \sqrt{5}$

Decimal Form:

$- 33.91485505 \dots$

Simplify 3 square root of 20(2 square root of 5-7)

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