Simplify square root of 7y( square root of 27y+5 square root of 12y)

$\sqrt{7 y} (\sqrt{27 y} + 5 \sqrt{12 y})$

Step 1

Simplify each term.

Rewrite $27 y$ as $3^{2} \cdot (3 y)$ .

Factor $9$ out of $27$ .

$\sqrt{7 y} (\sqrt{9 (3) y} + 5 \sqrt{12 y})$

Rewrite $9$ as $3^{2}$ .

$\sqrt{7 y} (\sqrt{3^{2} \cdot 3 y} + 5 \sqrt{12 y})$

Add parentheses.

$\sqrt{7 y} (\sqrt{3^{2} \cdot (3 y)} + 5 \sqrt{12 y})$

Pull terms out from under the radical.

$\sqrt{7 y} (3 \sqrt{3 y} + 5 \sqrt{12 y})$

Rewrite $12 y$ as $2^{2} \cdot (3 y)$ .

Factor $4$ out of $12$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $5$ .

$\sqrt{7 y} (3 \sqrt{3 y} + 10 \sqrt{3 y})$

Step 2

Simplify by adding terms.

Add $3 \sqrt{3 y}$ and $10 \sqrt{3 y}$ .

$\sqrt{7 y} (13 \sqrt{3 y})$

Rewrite using the commutative property of multiplication.

$13 \sqrt{7 y} \sqrt{3 y}$

Step 3

Multiply $13 \sqrt{7 y} \sqrt{3 y}$ .

Combine using the product rule for radicals.

$13 \sqrt{3 y (7 y)}$

Multiply $7$ by $3$ .

$13 \sqrt{21 y \cdot y}$

Raise $y$ to the power of $1$ .

$13 \sqrt{21 (y^{1} y)}$

Raise $y$ to the power of $1$ .

$13 \sqrt{21 (y^{1} y^{1})}$

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

$13 \sqrt{21 y^{1 + 1}}$

Add $1$ and $1$ .

$13 \sqrt{21 y^{2}}$

Step 4

Reorder $21$ and $y^{2}$ .

$13 \sqrt{y^{2} \cdot 21}$

Step 5

Pull terms out from under the radical.

$13 y \sqrt{21}$

Simplify square root of 7y( square root of 27y+5 square root of 12y)

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