Simplify (2 square root of 8+3 square root of 5)(7 square root of 5)

$(2 \sqrt{8} + 3 \sqrt{5}) (7 \sqrt{5})$

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $2$ .

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

Apply the distributive property.

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

Multiply $4 \sqrt{2} (7 \sqrt{5})$ .

Multiply $7$ by $4$ .

$28 \sqrt{2} \sqrt{5} + 3 \sqrt{5} (7 \sqrt{5})$

Combine using the product rule for radicals.

$28 \sqrt{5 \cdot 2} + 3 \sqrt{5} (7 \sqrt{5})$

Multiply $5$ by $2$ .

$28 \sqrt{10} + 3 \sqrt{5} (7 \sqrt{5})$

Multiply $3 \sqrt{5} (7 \sqrt{5})$ .

Multiply $7$ by $3$ .

$28 \sqrt{10} + 21 \sqrt{5} \sqrt{5}$

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

$28 \sqrt{10} + 21 ({\sqrt{5}}^{1} \sqrt{5})$

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

$28 \sqrt{10} + 21 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$28 \sqrt{10} + 21 {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

$28 \sqrt{10} + 21 {\sqrt{5}}^{2}$

Simplify each term.

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

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

$28 \sqrt{10} + 21 {(5^{\frac{1}{2}})}^{2}$

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

$28 \sqrt{10} + 21 \cdot 5^{\frac{1}{2} \cdot 2}$

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

$28 \sqrt{10} + 21 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$28 \sqrt{10} + 21 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$28 \sqrt{10} + 21 \cdot 5^{1}$

Evaluate the exponent.

$28 \sqrt{10} + 21 \cdot 5$

Multiply $21$ by $5$ .

$28 \sqrt{10} + 105$

The result can be shown in multiple forms.

Exact Form:

$28 \sqrt{10} + 105$

Decimal Form:

$193.54377448 \dots$

Simplify (2 square root of 8+3 square root of 5)(7 square root of 5)

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