Solve (sqrt80 sqrt40) / sqrt 5

Question

Calculate the value

810

Alternative Form

\approx 25.298221

Evaluate

\frac{80 \times 40}{5}

Simplify the root

More Steps

Evaluate

80

Write the expression as a product where the root of one of the factors can be evaluated

16 \times 5

Write the number in exponential form with the base of 4

4^{2} \times 5

The root of a product is equal to the product of the roots of each factor

4^{2} \times 5

Reduce the index of the radical and exponent with 2

45

\frac{4 5 \times 40}{5}

Simplify the root

More Steps

Evaluate

40

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 10

Write the number in exponential form with the base of 2

2^{2} \times 10

The root of a product is equal to the product of the roots of each factor

2^{2} \times 10

Reduce the index of the radical and exponent with 2

210

\frac{4 5 \times 2 10}{5}

Multiply the numbers

More Steps

Evaluate

45 \times 210

Multiply the terms

85 \times 10

Rewrite the expression

More Steps

Evaluate

5 \times 10

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

5 \times 10

Calculate the product

50

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 2

Write the number in exponential form with the base of 5

5^{2} \times 2

The root of a product is equal to the product of the roots of each factor

5^{2} \times 2

Reduce the index of the radical and exponent with 2

52

8 \times 52

Multiply the terms

402

\frac{40 2}{5}

Multiply by the Conjugate

\frac{40 2 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

2 \times 5

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

2 \times 5

Calculate the product

10

\frac{40 10}{5 \times 5}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{40 10}{5}

Solution

810

Alternative Form

\approx 25.298221

Show Solution