Simplify 3 square root of 7(1- square root of 7)

$3 \sqrt{7} (1 - \sqrt{7})$

Apply the distributive property.

$3 \sqrt{7} \cdot 1 + 3 \sqrt{7} (- \sqrt{7})$

Multiply $3$ by $1$ .

$3 \sqrt{7} + 3 \sqrt{7} (- \sqrt{7})$

Multiply $3 \sqrt{7} (- \sqrt{7})$ .

Multiply $- 1$ by $3$ .

$3 \sqrt{7} - 3 \sqrt{7} \sqrt{7}$

Raise $\sqrt{7}$ to the power of $1$ .

$3 \sqrt{7} - 3 ({\sqrt{7}}^{1} \sqrt{7})$

Raise $\sqrt{7}$ to the power of $1$ .

$3 \sqrt{7} - 3 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

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

$3 \sqrt{7} - 3 {\sqrt{7}}^{1 + 1}$

Add $1$ and $1$ .

$3 \sqrt{7} - 3 {\sqrt{7}}^{2}$

Simplify each term.

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$3 \sqrt{7} - 3 {(7^{\frac{1}{2}})}^{2}$

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

$3 \sqrt{7} - 3 \cdot 7^{\frac{1}{2} \cdot 2}$

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

$3 \sqrt{7} - 3 \cdot 7^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 \sqrt{7} - 3 \cdot 7^{\frac{2}{2}}$

Rewrite the expression.

$3 \sqrt{7} - 3 \cdot 7^{1}$

Evaluate the exponent.

$3 \sqrt{7} - 3 \cdot 7$

Multiply $- 3$ by $7$ .

$3 \sqrt{7} - 21$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{7} - 21$

Decimal Form:

$- 13.06274606 \dots$