Solve r^64-25 - ScanMath

Question

Simplify the expression

4 r^{6} - 25

Evaluate

r^{6} \times 4 - 25

Solution

4 r^{6} - 25

Show Solution

(2 r^{3} - 5) (2 r^{3} + 5)

Evaluate

r^{6} \times 4 - 25

Use the commutative property to reorder the terms

4 r^{6} - 25

Rewrite the expression in exponential form

(2 r^{3})^{2} - 5^{2}

Solution

(2 r^{3} - 5) (2 r^{3} + 5)

Show Solution

r_{1} = - \frac{3 20}{2}, r_{2} = \frac{3 20}{2}

Alternative Form

r_{1} \approx - 1.357209, r_{2} \approx 1.357209

Evaluate

r^{6} \times 4 - 25

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

r^{6} \times 4 - 25 = 0

Use the commutative property to reorder the terms

4 r^{6} - 25 = 0

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

4 r^{6} = 0 + 25

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

4 r^{6} = 25

Divide both sides

\frac{4 r ^{6}}{4} = \frac{25}{4}

Divide the numbers

r^{6} = \frac{25}{4}

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

r = \pm 6 \frac{25}{4}

Simplify the expression

More Steps

Evaluate

6 \frac{25}{4}

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

\frac{6 25}{6 4}

Simplify the radical expression

More Steps

Evaluate

625

Write the number in exponential form with the base of 5

6 5^{2}

Reduce the index of the radical and exponent with 2

35

\frac{3 5}{6 4}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 2

6 2^{2}

Reduce the index of the radical and exponent with 2

32

\frac{3 5}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 5 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 34

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

3 5 \times 4

Calculate the product

320

\frac{3 20}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 20}{2}

r = \pm \frac{3 20}{2}

Separate the equation into 2 possible cases

r = \frac{3 20}{2} r = - \frac{3 20}{2}

Solution

r_{1} = - \frac{3 20}{2}, r_{2} = \frac{3 20}{2}

Alternative Form

r_{1} \approx - 1.357209, r_{2} \approx 1.357209

Show Solution