What is sqrt(5-\sqrt{7)}*sqrt(3+\sqrt{7)} ?

The solution to sqrt(5-\sqrt{7)}*sqrt(3+\sqrt{7)} is 1+sqrt(7)

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simplify sqrt(5-\sqrt{7)}*sqrt(3+\sqrt{7)}

simplify

5 - 7 \cdot 3 + 7

1 + 7

Decimal Notation

3.64575 \dots

Solution steps

5 - 7 3 + 7

Apply radical rule:

a b = a \cdot b

5 - 7 3 + 7 = (5 - 7) (3 + 7)

= (5 - 7) (3 + 7)

(5 - 7) (3 + 7) = 8 + 27

= 8 + 27

= 7 + 27 + 1

= (7)^{2} + 27 + (1)^{2}

1 = 1

= (7)^{2} + 27 + 1^{2}

27 \cdot 1 = 27

= (7)^{2} + 27 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(7)^{2} + 27 \cdot 1 + 1^{2} = (7 + 1)^{2}

= (7 + 1)^{2}

Apply radical rule:

(7 + 1)^{2} = 7 + 1

= 7 + 1

e^{- 2 p}

e^{- 43}

e^{- 2 z}

e^{- 4 x} \cdot 5 e^{5 x}

5.2 \cdot 1 0^{- 6}

What is sqrt(5-\sqrt{7)}*sqrt(3+\sqrt{7)} ?
The solution to sqrt(5-\sqrt{7)}*sqrt(3+\sqrt{7)} is 1+sqrt(7)