Simplify 5(4-5^(1/2))

$5 (4 - 5^{\frac{1}{2}})$

Step 1

Apply the distributive property.

$5 \cdot 4 + 5 (- 5^{\frac{1}{2}})$

Step 2

Multiply $5$ by $4$ .

$20 + 5 (- 5^{\frac{1}{2}})$

Step 3

Multiply $5$ by $5^{\frac{1}{2}}$ by adding the exponents.

Move $5^{\frac{1}{2}}$ .

$20 + 5^{\frac{1}{2}} \cdot 5 \cdot - 1$

Multiply $5^{\frac{1}{2}}$ by $5$ .

Raise $5$ to the power of $1$ .

$20 + 5^{\frac{1}{2}} \cdot 5^{1} \cdot - 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$20 + 5^{\frac{1}{2} + 1} \cdot - 1$

Write $1$ as a fraction with a common denominator.

$20 + 5^{\frac{1}{2} + \frac{2}{2}} \cdot - 1$

Combine the numerators over the common denominator.

$20 + 5^{\frac{1 + 2}{2}} \cdot - 1$

Add $1$ and $2$ .

$20 + 5^{\frac{3}{2}} \cdot - 1$

Step 4

Simplify each term.

Move $- 1$ to the left of $5^{\frac{3}{2}}$ .

$20 - 1 \cdot 5^{\frac{3}{2}}$

Rewrite $- 1 \cdot 5^{\frac{3}{2}}$ as $- 5^{\frac{3}{2}}$ .

$20 - 5^{\frac{3}{2}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$20 - 5^{\frac{3}{2}}$

Decimal Form:

$8.81966011 \dots$