Square root 48 simplified.
Understand the Problem
The question is asking us to simplify the square root of 48. This involves finding the prime factors of 48 and re-expressing the square root in simpler terms.
Answer
4\sqrt{3}
Answer for screen readers
The final answer is 4\sqrt{3}
Steps to Solve
- Find the prime factors of 48
The number 48 can be factored into prime factors as follows: $$48 = 2 imes 24 = 2 imes 2 imes 12 = 2 imes 2 imes 2 imes 6 = 2 imes 2 imes 2 imes 2 imes 3 = 2^4 imes 3$$
- Apply the square root to the prime factors
Recall that the square root of a product is the product of the square roots: $$\sqrt{48} = \sqrt{2^4 \times 3}$$
- Separate the square root into two parts
We can separate this into two square roots: $$\sqrt{2^4 \times 3} = \sqrt{2^4} \times \sqrt{3}$$
- Simplify the square roots
Since the square root of a power is half the exponent: $$\sqrt{2^4} = 2^2 = 4$$, therefore, $$\sqrt{48} = 4 \times \sqrt{3}$$
The final answer is 4\sqrt{3}
More Information
Simplifying square roots makes expressions easier to understand.
Tips
A common mistake is incorrectly pulling out terms from under the square root by not properly applying the square root to the prime factors.
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