Solve (5n^3-7)^2 - ScanMath

Question

Simplify the expression

25 n^{6} - 70 n^{3} + 49

Evaluate

(5 n^{3} - 7)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

(5 n^{3})^{2} - 2 \times 5 n^{3} \times 7 + 7^{2}

Solution

25 n^{6} - 70 n^{3} + 49

Show Solution

n = \frac{3 175}{5}

Alternative Form

n \approx 1.118689

Evaluate

(5 n^{3} - 7)^{2}

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

(5 n^{3} - 7)^{2} = 0

The only way a power can be 0 is when the base equals 0

5 n^{3} - 7 = 0

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

5 n^{3} = 0 + 7

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

5 n^{3} = 7

Divide both sides

\frac{5 n ^{3}}{5} = \frac{7}{5}

Divide the numbers

n^{3} = \frac{7}{5}

Take the 3 -th root on both sides of the equation

3 n^{3} = 3 \frac{7}{5}

Calculate

n = 3 \frac{7}{5}

Solution

More Steps

Evaluate

3 \frac{7}{5}

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

\frac{3 7}{3 5}

Multiply by the Conjugate

\frac{3 7 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 7 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 325

The product of roots with the same index is equal to the root of the product

3 7 \times 25

Calculate the product

3175

\frac{3 175}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

The product of roots with the same index is equal to the root of the product

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 175}{5}

n = \frac{3 175}{5}

Alternative Form

n \approx 1.118689

Show Solution