Simplify the square root of -20 using i

Question

asked Feb 16, 2024 160k views

1 Answer

Alister Bulman · Answer 1 · 2024-02-22T06:07:09+0000

Answer:

$√(-20)=2 √(5)\;i$

Explanation:

The imaginary unit is denoted by the letter
and is defined as the square root of -1:

$\boxed{i=√(-1)}$

To simplify the square root of -20, first rewrite -20 as the product of -1 and 20:

$√(-20)=√(-1 \cdot 20)$

Now rewrite 20 as the product of prime numbers:

$√(-20)=√(-1 \cdot 2^2 \cdot 5)$

$\textsf{Apply the radical rule:} \quad √(ab)=√(a)√(b)$

√(-20)=√(-1) √(2^2) √(5)

$\textsf{Apply the radical rule:} \quad √(a^2)=a, \quad a \geq 0$

$√(-20)=√(-1) \cdot 2 √(5)$

$\textsf{Finally, apply}\;\;√(-1)=i$

$√(-20)=i\cdot 2 √(5)$

$√(-20)=2 √(5)\;i$