What is the cube root of 1728?
12
To find the cube root of 1728, express it as a product of prime factors: \(1728 = 2^6 \times 3^3\).
So, \(\sqrt[3]{1728} = \sqrt[3]{2^6 \times 3^3} = 2^2 \times 3 = 4 \times 3 = 12\).
Verification: \(12^3 = 12 \times 12 \times 12 = 1728\).
Simplify the following expression:
\[ \left(\frac{x^2}{x^m}\right)^{1+m} \left(\frac{x^m}{x^n}\right)^{m+n} \left(\frac{x^n}{x^l}\right)^{n+l} \]
If 2ˣ = 4ˣ⁻¹, find x.
Evaluate √(19 - 6√10) + 3
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
The expression \(\frac{{15\left( {\sqrt {10} + \sqrt 5 } \right)}}{{\sqrt {10\;} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\) is equal to:
Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\) . Then √x is equal to:
If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\) where x > 0, then the value of x is equal to:
What is the value of \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?