Square root of 160 in radical form.
Understand the Problem
The question is asking for the square root of the number 160 expressed in radical form. This involves simplifying the square root by factoring out perfect squares.
Answer
\( 4\sqrt{10} \)
Answer for screen readers
The simplified radical form of the square root of 160 is ( 4\sqrt{10} ).
Steps to Solve
-
Identify the number to simplify
We start with the square root of the number 160, which can be expressed as:
$$ \sqrt{160} $$ -
Factor the number into prime factors
Next, we need to break down 160 into its prime factors.
160 can be factored as:
$$ 160 = 16 \times 10 = 16 \times 2 \times 5 $$
We see that 16 is a perfect square. -
Express the square root as a product
Now we can rewrite the square root of 160 as the product of the square roots of its factors:
$$ \sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} $$ -
Simplify the square root
Since $\sqrt{16}$ equals 4 (because $4 \times 4 = 16$), we have:
$$ \sqrt{160} = 4 \times \sqrt{10} $$ -
Write the final simplified form
Thus, the square root of 160 simplified in radical form is:
$$ 4\sqrt{10} $$
The simplified radical form of the square root of 160 is ( 4\sqrt{10} ).
More Information
Simplifying square roots is a common technique in math, especially useful in algebra. Knowing how to factor and identify perfect squares can help simplify expressions effectively.
Tips
- A common mistake is forgetting to simplify the square root completely or misidentifying the perfect squares. Always double-check the factors for perfect squares.
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