Solve B^44202-10-15

Question

Simplify the expression

4202 B^{4} - 25

Evaluate

B^{4} \times 4202 - 10 - 15

Use the commutative property to reorder the terms

4202 B^{4} - 10 - 15

Solution

4202 B^{4} - 25

Show Solution

B_{1} = - \frac{4 25 \times 420 2 ^{3}}{4202}, B_{2} = \frac{4 25 \times 420 2 ^{3}}{4202}

Alternative Form

B_{1} \approx - 0.277729, B_{2} \approx 0.277729

Evaluate

B^{4} \times 4202 - 10 - 15

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

B^{4} \times 4202 - 10 - 15 = 0

Use the commutative property to reorder the terms

4202 B^{4} - 10 - 15 = 0

Subtract the numbers

4202 B^{4} - 25 = 0

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

4202 B^{4} = 0 + 25

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

4202 B^{4} = 25

Divide both sides

\frac{4202 B ^{4}}{4202} = \frac{25}{4202}

Divide the numbers

B^{4} = \frac{25}{4202}

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

B = \pm 4 \frac{25}{4202}

Simplify the expression

More Steps

Evaluate

4 \frac{25}{4202}

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

\frac{4 25}{4 4202}

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 4202}

Multiply by the Conjugate

\frac{5 \times 4 420 2 ^{3}}{4 4202 \times 4 420 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

5 \times 4 420 2^{3}

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

4 5^{2} \times 4 420 2^{3}

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

4 5^{2} \times 420 2^{3}

Calculate the product

4 25 \times 420 2^{3}

\frac{4 25 \times 420 2 ^{3}}{4 4202 \times 4 420 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

44202 \times 4 420 2^{3}

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

4 4202 \times 420 2^{3}

Calculate the product

4 420 2^{4}

Reduce the index of the radical and exponent with 4

4202

\frac{4 25 \times 420 2 ^{3}}{4202}

B = \pm \frac{4 25 \times 420 2 ^{3}}{4202}

Separate the equation into 2 possible cases

B = \frac{4 25 \times 420 2 ^{3}}{4202} B = - \frac{4 25 \times 420 2 ^{3}}{4202}

Solution

B_{1} = - \frac{4 25 \times 420 2 ^{3}}{4202}, B_{2} = \frac{4 25 \times 420 2 ^{3}}{4202}

Alternative Form

B_{1} \approx - 0.277729, B_{2} \approx 0.277729

Show Solution