Solve (sqrt(5) * sqrt(3)) / (sqrt(5) - sqrt(3))

Question

Calculate the value

\frac{5 3 + 3 5}{2}

Alternative Form

\approx 7.684229

Evaluate

\frac{5 \times 3}{5 - 3}

Multiply the numbers

More Steps

Evaluate

5 \times 3

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

5 \times 3

Calculate the product

15

\frac{15}{5 - 3}

Multiply by the Conjugate

\frac{15 \times ( 5 + 3 )}{( 5 - 3 ) ( 5 + 3 )}

Multiply the numbers

More Steps

Rewrite the expression

(5 - 3) (5 + 3)

Use (a - b) (a + b) = a^{2} - b^{2} to simplify the product

(5)^{2} - (3)^{2}

Reduce the index of the radical and exponent with 2

5 - (3)^{2}

Reduce the index of the radical and exponent with 2

5 - 3

Subtract the numbers

2

\frac{15 \times ( 5 + 3 )}{2}

Solution

More Steps

Evaluate

15 \times (5 + 3)

Apply the distributive property

15 \times 5 + 15 \times 3

Multiply the numbers

More Steps

Evaluate

15 \times 5

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

15 \times 5

Calculate the product

75

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

25 \times 3

Write the number in exponential form with the base of 5

5^{2} \times 3

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

5^{2} \times 3

Reduce the index of the radical and exponent with 2

53

53 + 15 \times 3

Multiply the numbers

More Steps

Evaluate

15 \times 3

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

15 \times 3

Calculate the product

45

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

9 \times 5

Write the number in exponential form with the base of 3

3^{2} \times 5

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

3^{2} \times 5

Reduce the index of the radical and exponent with 2

35

53 + 35

\frac{5 3 + 3 5}{2}

Alternative Form

\approx 7.684229

Show Solution