Solve r^4626-25 - ScanMath

Question

Simplify the expression

626 r^{4} - 25

Evaluate

r^{4} \times 626 - 25

Solution

626 r^{4} - 25

Show Solution

r_{1} = - \frac{4 25 \times 62 6 ^{3}}{626}, r_{2} = \frac{4 25 \times 62 6 ^{3}}{626}

Alternative Form

r_{1} \approx - 0.447035, r_{2} \approx 0.447035

Evaluate

r^{4} \times 626 - 25

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

r^{4} \times 626 - 25 = 0

Use the commutative property to reorder the terms

626 r^{4} - 25 = 0

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

626 r^{4} = 0 + 25

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

626 r^{4} = 25

Divide both sides

\frac{626 r ^{4}}{626} = \frac{25}{626}

Divide the numbers

r^{4} = \frac{25}{626}

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

r = \pm 4 \frac{25}{626}

Simplify the expression

More Steps

Evaluate

4 \frac{25}{626}

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

\frac{4 25}{4 626}

Simplify the radical expression

More Steps

Evaluate

425

Write the number in exponential form with the base of 5

4 5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{4 626}

Multiply by the Conjugate

\frac{5 \times 4 62 6 ^{3}}{4 626 \times 4 62 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

5 \times 4 62 6^{3}

Use n a = mn a^{m} to expand the expression

4 5^{2} \times 4 62 6^{3}

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

4 5^{2} \times 62 6^{3}

Calculate the product

4 25 \times 62 6^{3}

\frac{4 25 \times 62 6 ^{3}}{4 626 \times 4 62 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

4626 \times 4 62 6^{3}

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

4 626 \times 62 6^{3}

Calculate the product

4 62 6^{4}

Reduce the index of the radical and exponent with 4

626

\frac{4 25 \times 62 6 ^{3}}{626}

r = \pm \frac{4 25 \times 62 6 ^{3}}{626}

Separate the equation into 2 possible cases

r = \frac{4 25 \times 62 6 ^{3}}{626} r = - \frac{4 25 \times 62 6 ^{3}}{626}

Solution

r_{1} = - \frac{4 25 \times 62 6 ^{3}}{626}, r_{2} = \frac{4 25 \times 62 6 ^{3}}{626}

Alternative Form

r_{1} \approx - 0.447035, r_{2} \approx 0.447035

Show Solution