Pre-Algebra Examples

$\sqrt{1.7 x^{2}} = \sqrt{1477.7}$

Step 1

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

${\sqrt{1.7 x^{2}}}^{2} = {\sqrt{1477.7}}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{1.7 x^{2}}$ as ${(1.7 x^{2})}^{\frac{1}{2}}$ .

${({(1.7 x^{2})}^{\frac{1}{2}})}^{2} = {\sqrt{1477.7}}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(1.7 x^{2})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(1.7 x^{2})}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(1.7 x^{2})}^{\frac{1}{2} \cdot 2} = {\sqrt{1477.7}}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(1.7 x^{2})}^{\frac{1}{2} \cdot 2} = {\sqrt{1477.7}}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(1.7 x^{2})}^{1} = {\sqrt{1477.7}}^{2}$

Step 2.2.1.2

Simplify.

$1.7 x^{2} = {\sqrt{1477.7}}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Rewrite ${\sqrt{1477.7}}^{2}$ as $1477.7$ .

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Step 2.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{1477.7}$ as ${1477.7}^{\frac{1}{2}}$ .

$1.7 x^{2} = {({1477.7}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2

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

$1.7 x^{2} = {1477.7}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.3

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

$1.7 x^{2} = {1477.7}^{\frac{2}{2}}$

Step 2.3.1.4

Cancel the common factor of $2$ .

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Step 2.3.1.4.1

Cancel the common factor.

$1.7 x^{2} = {1477.7}^{\frac{2}{2}}$

Step 2.3.1.4.2

Rewrite the expression.

$1.7 x^{2} = {1477.7}^{1}$

Step 2.3.1.5

Evaluate the exponent.

$1.7 x^{2} = 1477.7$

Step 3

Solve for $x$ .

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Step 3.1

Divide each term in $1.7 x^{2} = 1477.7$ by $1.7$ and simplify.

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Step 3.1.1

Divide each term in $1.7 x^{2} = 1477.7$ by $1.7$ .

$\frac{1.7 x^{2}}{1.7} = \frac{1477.7}{1.7}$

Step 3.1.2

Simplify the left side.

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Step 3.1.2.1

Cancel the common factor of $1.7$ .

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Step 3.1.2.1.1

Cancel the common factor.

$\frac{1.7 x^{2}}{1.7} = \frac{1477.7}{1.7}$

Step 3.1.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{1477.7}{1.7}$

Step 3.1.3

Simplify the right side.

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Step 3.1.3.1

Divide $1477.7$ by $1.7$ .

$x^{2} = 869.23529411$

Step 3.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{869.23529411}$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{869.23529411}$

Step 3.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{869.23529411}$

Step 3.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{869.23529411}, - \sqrt{869.23529411}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{869.23529411}, - \sqrt{869.23529411}$

Decimal Form:

$x = 29.48279657 \dots, - 29.48279657 \dots$