Solve sqrt(2 / 100) * (1 - sqrt(1 / 50)) * 2

Question

Calculate the value

\frac{5 2 - 1}{25}

Alternative Form

\approx 0.242843

Evaluate

\frac{2}{100} \times (1 - \frac{1}{50}) \times 2

Simplify the root

More Steps

Evaluate

\frac{1}{50}

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

\frac{1}{50}

Simplify the radical expression

\frac{1}{50}

Simplify the radical expression

More Steps

Evaluate

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

\frac{1}{5 2}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

52 \times 2

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

5 \times 2

Multiply the terms

10

\frac{2}{10}

\frac{2}{100} \times (1 - \frac{2}{10}) \times 2

Subtract the numbers

More Steps

Simplify

1 - \frac{2}{10}

Reduce fractions to a common denominator

\frac{10}{10} - \frac{2}{10}

Write all numerators above the common denominator

\frac{10 - 2}{10}

\frac{2}{100} \times \frac{10 - 2}{10} \times 2

Cancel out the common factor 2

\frac{1}{50} \times \frac{10 - 2}{10} \times 2

Simplify the root

More Steps

Evaluate

\frac{1}{50}

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

\frac{1}{50}

Simplify the radical expression

\frac{1}{50}

Simplify the radical expression

More Steps

Evaluate

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

\frac{1}{5 2}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

52 \times 2

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

5 \times 2

Multiply the terms

10

\frac{2}{10}

\frac{2}{10} \times \frac{10 - 2}{10} \times 2

Multiply the terms

More Steps

Evaluate

\frac{2}{10} \times \frac{10 - 2}{10}

To multiply the fractions,multiply the numerators and denominators separately

\frac{2 \times ( 10 - 2 )}{10 \times 10}

Multiply the numbers

More Steps

Evaluate

2 \times (10 - 2)

Apply the distributive property

2 \times 10 - 2 \times 2

Multiply the numbers

102 - 2 \times 2

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

102 - 2

\frac{10 2 - 2}{10 \times 10}

Multiply the numbers

\frac{10 2 - 2}{100}

Rewrite the expression

\frac{2 ( 5 2 - 1 )}{100}

Cancel out the common factor 2

\frac{5 2 - 1}{50}

\frac{5 2 - 1}{50} \times 2

Reduce the numbers

\frac{5 2 - 1}{25} \times 1

Solution

\frac{5 2 - 1}{25}

Alternative Form

\approx 0.242843

Show Solution