Basic Math Examples

$\sqrt{v} + 3 t = 16$

Step 1

Subtract $3 t$ from both sides of the equation.

$\sqrt{v} = 16 - 3 t$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{v}}^{2} = {(16 - 3 t)}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

${(v^{\frac{1}{2}})}^{2} = {(16 - 3 t)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(v^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${(v^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

$v^{\frac{1}{2} \cdot 2} = {(16 - 3 t)}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$v^{\frac{1}{2} \cdot 2} = {(16 - 3 t)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$v^{1} = {(16 - 3 t)}^{2}$

Step 3.2.1.2

Simplify.

$v = {(16 - 3 t)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(16 - 3 t)}^{2}$ .

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Step 3.3.1.1

Rewrite ${(16 - 3 t)}^{2}$ as $(16 - 3 t) (16 - 3 t)$ .

$v = (16 - 3 t) (16 - 3 t)$

Step 3.3.1.2

Expand $(16 - 3 t) (16 - 3 t)$ using the FOIL Method.

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Step 3.3.1.2.1

Apply the distributive property.

$v = 16 (16 - 3 t) - 3 t (16 - 3 t)$

Step 3.3.1.2.2

Apply the distributive property.

$v = 16 \cdot 16 + 16 (- 3 t) - 3 t (16 - 3 t)$

Step 3.3.1.2.3

Apply the distributive property.

$v = 16 \cdot 16 + 16 (- 3 t) - 3 t \cdot 16 - 3 t (- 3 t)$

Step 3.3.1.3

Simplify and combine like terms.

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Step 3.3.1.3.1

Simplify each term.

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Step 3.3.1.3.1.1

Multiply $16$ by $16$ .

$v = 256 + 16 (- 3 t) - 3 t \cdot 16 - 3 t (- 3 t)$

Step 3.3.1.3.1.2

Multiply $- 3$ by $16$ .

$v = 256 - 48 t - 3 t \cdot 16 - 3 t (- 3 t)$

Step 3.3.1.3.1.3

Multiply $16$ by $- 3$ .

$v = 256 - 48 t - 48 t - 3 t (- 3 t)$

Step 3.3.1.3.1.4

Rewrite using the commutative property of multiplication.

$v = 256 - 48 t - 48 t - 3 \cdot - 3 t \cdot t$

Step 3.3.1.3.1.5

Multiply $t$ by $t$ by adding the exponents.

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Step 3.3.1.3.1.5.1

Move $t$ .

$v = 256 - 48 t - 48 t - 3 \cdot - 3 (t \cdot t)$

Step 3.3.1.3.1.5.2

Multiply $t$ by $t$ .

$v = 256 - 48 t - 48 t - 3 \cdot - 3 t^{2}$

Step 3.3.1.3.1.6

Multiply $- 3$ by $- 3$ .

$v = 256 - 48 t - 48 t + 9 t^{2}$

Step 3.3.1.3.2

Subtract $48 t$ from $- 48 t$ .

$v = 256 - 96 t + 9 t^{2}$