Solve (x^frac{1{2}}-2)^2

$$( x ^ { \frac { 1 } { 2 } } - 2 ) ^ { 2 }$$

Evaluate

$$\left(\sqrt{x}-2\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{\frac{1}{2}}-2\right)^{2}.

$$\left(x^{\frac{1}{2}}\right)^{2}-4x^{\frac{1}{2}}+4$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$x^{1}-4x^{\frac{1}{2}}+4$$

Calculate x to the power of 1 and get x.

$$x-4x^{\frac{1}{2}}+4$$

Expand

$$x-4\sqrt{x}+4$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{\frac{1}{2}}-2\right)^{2}.

$$\left(x^{\frac{1}{2}}\right)^{2}-4x^{\frac{1}{2}}+4$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$x^{1}-4x^{\frac{1}{2}}+4$$

Calculate x to the power of 1 and get x.

$$x-4x^{\frac{1}{2}}+4$$