Evaluate (5/4(424333-10220^2))^(1/2)

${(\frac{5}{4} (424333 - 10220^{2}))}^{\frac{1}{2}}$

Step 1

Simplify each term.

Raise $10220$ to the power of $2$ .

${(\frac{5}{4} \cdot (424333 - 1 \cdot 104448400))}^{\frac{1}{2}}$

Multiply $- 1$ by $104448400$ .

${(\frac{5}{4} \cdot (424333 - 104448400))}^{\frac{1}{2}}$

Step 2

Subtract $104448400$ from $424333$ .

${(\frac{5}{4} \cdot - 104024067)}^{\frac{1}{2}}$

Step 3

Multiply $\frac{5}{4} \cdot - 104024067$ .

Combine $\frac{5}{4}$ and $- 104024067$ .

${(\frac{5 \cdot - 104024067}{4})}^{\frac{1}{2}}$

Multiply $5$ by $- 104024067$ .

${(\frac{- 520120335}{4})}^{\frac{1}{2}}$

Step 4

Move the negative in front of the fraction.

${(- \frac{520120335}{4})}^{\frac{1}{2}}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{520120335}{4}$ .

${(- 1)}^{\frac{1}{2}} {(\frac{520120335}{4})}^{\frac{1}{2}}$

Apply the product rule to $\frac{520120335}{4}$ .

${(- 1)}^{\frac{1}{2}} \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 6

Rewrite ${(- 1)}^{\frac{1}{2}}$ as $\sqrt{{(- 1)}^{1}}$ .

$\sqrt{{(- 1)}^{1}} \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 7

Evaluate the exponent.

$\sqrt{- 1} \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 8

Rewrite $\sqrt{- 1}$ as $i$ .

$i \frac{520120335^{\frac{1}{2}}}{4^{\frac{1}{2}}}$

Step 9

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$i \frac{520120335^{\frac{1}{2}}}{{(2^{2})}^{\frac{1}{2}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$i \frac{520120335^{\frac{1}{2}}}{2^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$i \frac{520120335^{\frac{1}{2}}}{2^{2 (\frac{1}{2})}}$

Rewrite the expression.

$i \frac{520120335^{\frac{1}{2}}}{2^{1}}$

Evaluate the exponent.

$i \frac{520120335^{\frac{1}{2}}}{2}$

Step 10

Combine $i$ and $\frac{520120335^{\frac{1}{2}}}{2}$ .

$\frac{i \cdot 520120335^{\frac{1}{2}}}{2}$

Evaluate (5/4(424333-10220^2))^(1/2)

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