simplify sqrt(4^2+2^2) — step-by-step solution

Let's reduce:

\sqrt{4^{2} + 2^{2}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

4^{2}

4 \times 4

16

2^{2}

2 \times 2

4

\sqrt{16 + 4}

ⓘ Parentheses are computed first:

16 + 4

20

\sqrt{20}

ⓘ We look for the largest square dividing

20

4

2^{2}

, and take it out of the root:

\sqrt{20}

\sqrt{4 \times 5}

\sqrt{4} \times \sqrt{5}

2 \times \sqrt{5}

▶Simplified form:

2 \times \sqrt{5}

The numeric value of:

2 \times \sqrt{5}

is:

2 \times \approx 2.2361

▷

\approx 4.4721