Solve (3z 10)^2-10

Question

Simplify the expression

900 z^{2} - 10

Evaluate

(3 z \times 10)^{2} - 10

Multiply the terms

(30 z)^{2} - 10

Solution

900 z^{2} - 10

Show Solution

Factor the expression

10 (90 z^{2} - 1)

Evaluate

(3 z \times 10)^{2} - 10

Multiply the terms

(30 z)^{2} - 10

Simplify

More Steps

Evaluate

(30 z)^{2}

Rewrite the expression

30 z \times 30 z

Multiply the numbers

900 z \times z

Multiply the terms

900 z^{2}

900 z^{2} - 10

Solution

10 (90 z^{2} - 1)

Show Solution

Find the roots

z_{1} = - \frac{10}{30}, z_{2} = \frac{10}{30}

Alternative Form

z_{1} \approx - 0.105409, z_{2} \approx 0.105409

Evaluate

(3 z \times 10)^{2} - 10

To find the roots of the expression,set the expression equal to 0

(3 z \times 10)^{2} - 10 = 0

Multiply the terms

(30 z)^{2} - 10 = 0

Rewrite the expression

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Simplify

(30 z)^{2} - 10

Rewrite the expression

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Evaluate

(30 z)^{2}

To raise a product to a power,raise each factor to that power

3 0^{2} z^{2}

Evaluate the power

900 z^{2}

900 z^{2} - 10

900 z^{2} - 10 = 0

Move the constant to the right-hand side and change its sign

900 z^{2} = 0 + 10

Removing 0 doesn't change the value,so remove it from the expression

900 z^{2} = 10

Divide both sides

\frac{900 z ^{2}}{900} = \frac{10}{900}

Divide the numbers

z^{2} = \frac{10}{900}

Cancel out the common factor 10

z^{2} = \frac{1}{90}

Take the root of both sides of the equation and remember to use both positive and negative roots

z = \pm \frac{1}{90}

Simplify the expression

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Evaluate

\frac{1}{90}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{90}

Simplify the radical expression

\frac{1}{90}

Simplify the radical expression

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Evaluate

90

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 10

Write the number in exponential form with the base of 3

3^{2} \times 10

The root of a product is equal to the product of the roots of each factor

3^{2} \times 10

Reduce the index of the radical and exponent with 2

310

\frac{1}{3 10}

Multiply by the Conjugate

\frac{10}{3 10 \times 10}

Multiply the numbers

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Evaluate

310 \times 10

When a square root of an expression is multiplied by itself,the result is that expression

3 \times 10

Multiply the terms

30

\frac{10}{30}

z = \pm \frac{10}{30}

Separate the equation into 2 possible cases

z = \frac{10}{30} z = - \frac{10}{30}

Solution

z_{1} = - \frac{10}{30}, z_{2} = \frac{10}{30}

Alternative Form

z_{1} \approx - 0.105409, z_{2} \approx 0.105409

Show Solution