Simplify (2 square root of 3t+5)^2

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

Step 1

Rewrite ${(2 \sqrt{3 t} + 5)}^{2}$ as $(2 \sqrt{3 t} + 5) (2 \sqrt{3 t} + 5)$ .

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

Step 2

Expand $(2 \sqrt{3 t} + 5) (2 \sqrt{3 t} + 5)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2 \sqrt{3 t} (2 \sqrt{3 t})$ .

Multiply $2$ by $2$ .

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

Raise $\sqrt{3 t}$ to the power of $1$ .

$4 ({\sqrt{3 t}}^{1} \sqrt{3 t}) + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Raise $\sqrt{3 t}$ to the power of $1$ .

$4 ({\sqrt{3 t}}^{1} {\sqrt{3 t}}^{1}) + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

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

$4 {\sqrt{3 t}}^{1 + 1} + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Add $1$ and $1$ .

$4 {\sqrt{3 t}}^{2} + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Rewrite ${\sqrt{3 t}}^{2}$ as $3 t$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 t}$ as ${(3 t)}^{\frac{1}{2}}$ .

$4 {({(3 t)}^{\frac{1}{2}})}^{2} + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

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

$4 {(3 t)}^{\frac{1}{2} \cdot 2} + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

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

$4 {(3 t)}^{\frac{2}{2}} + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(3 t)}^{\frac{2}{2}} + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Rewrite the expression.

$4 {(3 t)}^{1} + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Simplify.

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

Multiply $3$ by $4$ .

$12 t + 2 \sqrt{3 t} \cdot 5 + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Multiply $5$ by $2$ .

$12 t + 10 \sqrt{3 t} + 5 (2 \sqrt{3 t}) + 5 \cdot 5$

Multiply $2$ by $5$ .

$12 t + 10 \sqrt{3 t} + 10 \sqrt{3 t} + 5 \cdot 5$

Multiply $5$ by $5$ .

$12 t + 10 \sqrt{3 t} + 10 \sqrt{3 t} + 25$

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

$12 t + 20 \sqrt{3 t} + 25$

Simplify (2 square root of 3t+5)^2

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