Solve y^222y - 21 = 0

Question

Solve the equation

y = \frac{3 10164}{22}

Alternative Form

y \approx 0.984613

Evaluate

y^{2} \times 22 y - 21 = 0

Multiply

More Steps

Evaluate

y^{2} \times 22 y

Multiply the terms with the same base by adding their exponents

y^{2 + 1} \times 22

Add the numbers

y^{3} \times 22

Use the commutative property to reorder the terms

22 y^{3}

22 y^{3} - 21 = 0

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

22 y^{3} = 0 + 21

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

22 y^{3} = 21

Divide both sides

\frac{22 y ^{3}}{22} = \frac{21}{22}

Divide the numbers

y^{3} = \frac{21}{22}

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

3 y^{3} = 3 \frac{21}{22}

Calculate

y = 3 \frac{21}{22}

Solution

More Steps

Evaluate

3 \frac{21}{22}

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

\frac{3 21}{3 22}

Multiply by the Conjugate

\frac{3 21 \times 3 2 2 ^{2}}{3 22 \times 3 2 2 ^{2}}

Simplify

\frac{3 21 \times 3 484}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3484

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

3 21 \times 484

Calculate the product

310164

\frac{3 10164}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

322 \times 3 2 2^{2}

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

3 22 \times 2 2^{2}

Calculate the product

3 2 2^{3}

Reduce the index of the radical and exponent with 3

22

\frac{3 10164}{22}

y = \frac{3 10164}{22}

Alternative Form

y \approx 0.984613

Show Solution