Find the value of \(\sqrt{388 + \sqrt{127 + \sqrt{289}}}\).
20
Step 1 – Innermost root: \(\sqrt{289} = 17\)
Step 2 – Middle root: \(\sqrt{127 + 17} = \sqrt{144} = 12\)
Step 3 – Outermost root: \(\sqrt{388 + 12} = \sqrt{400} = \mathbf{20}\)
If \(x = \sqrt{\dfrac{2 + \sqrt{3}}{2 - \sqrt{3}}}\), determine the value of \(x^2 + x - 9\).
Evaluate: \(\sqrt{12 + \sqrt{12 + \sqrt{12 + \cdots}}}\)
Simplify the expression: \(\sqrt{9 + 4\sqrt{5}}\)
Choose the correct relation:
(i) \(\sqrt{10} < 3.2\)
(ii) \(\sqrt{11} < \sqrt{12}\)
(iii) \(\sqrt{13} < \sqrt{14}\)
Simplify:
\(\dfrac{1}{\sqrt{7}-\sqrt{3}} + \dfrac{1}{\sqrt{7}+\sqrt{3}}\)
If \(\sqrt{a} + \sqrt{b} = 5\) and \(\sqrt{a} - \sqrt{b} = 1\), what are the values of a and b?
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
if 49 n + 49 n + 49 n + 49 n + 49 n + 49 n + 49 n = 7 2221 , then n = ?
If a x= b y= c zand b 2= ac then y =
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is: