Simplify square root of 7i* square root of 6i

$\sqrt{7} i \cdot \sqrt{6} i$

Step 1

Multiply $\sqrt{7} i (\sqrt{6} i)$ .

Combine using the product rule for radicals.

$\sqrt{6 \cdot 7} i i$

Multiply $6$ by $7$ .

$\sqrt{42} i i$

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

$\sqrt{42} (i^{1} i)$

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

$\sqrt{42} (i^{1} i^{1})$

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

$\sqrt{42} i^{1 + 1}$

Add $1$ and $1$ .

$\sqrt{42} i^{2}$

Step 2

Rewrite $i^{2}$ as $- 1$ .

$\sqrt{42} \cdot - 1$

Step 3

Move $- 1$ to the left of $\sqrt{42}$ .

$- 1 \cdot \sqrt{42}$

Step 4

Rewrite $- 1 \sqrt{42}$ as $- \sqrt{42}$ .

$- \sqrt{42}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{42}$

Decimal Form:

$- 6.48074069 \dots$