Question

$\sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7} } } } } }$
is equal to :
a) 0
b) 7
c) 7^63/64
d) 7^31/32​

Answer 1

Required Answer:-

Given to evaluate:

• $\sf \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7... \infty } } } } }$

Solution:

Let us assume that,

$\sf \implies x = \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7... \infty } } } } }$

Squaring both sides, we get,

$\sf \implies {x}^{2} = 7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7... \infty } } } }$

Now, if you look at the pattern, you can see that,

$\sf \implies {x}^{2} = 7x$

$\sf \implies {x}^{2} - 7x = 0$

$\sf \implies x(x - 7)= 0$

Therefore, either x = 0 or x - 7 = 0

But x = 0 is not possible. Thus,

➡ x = 7

★ Hence, the result is - 7

Answer:

• Result is - 7