Simplify √(16a^8b^24)/4.
Understand the Problem
The question is asking to simplify the expression √(16a^8b^24)/4. This involves applying the properties of square roots and simplifying the terms accordingly.
Answer
$a^4b^{12}$
Answer for screen readers
$a^4b^{12}$
Steps to Solve
- Simplifying the Square Root
Start by simplifying the expression under the square root.
The square root of a product can be separated: $$ \sqrt{16a^8b^{24}} = \sqrt{16} \cdot \sqrt{a^8} \cdot \sqrt{b^{24}} $$
Calculating each term:
- $\sqrt{16} = 4$
- $\sqrt{a^8} = a^{8/2} = a^4$
- $\sqrt{b^{24}} = b^{24/2} = b^{12}$
So we can rewrite it as: $$ \sqrt{16a^8b^{24}} = 4a^4b^{12} $$
- Dividing by the Denominator
Now, take the result from the previous step and divide it by 4: $$ \frac{\sqrt{16a^8b^{24}}}{4} = \frac{4a^4b^{12}}{4} $$
The 4's cancel out: $$ a^4b^{12} $$
- Final Expression
The final simplified expression is: $$ a^4b^{12} $$
$a^4b^{12}$
More Information
This simplification shows how to efficiently use properties of square roots to simplify expressions. The expression $a^4b^{12}$ reveals the simplified terms, which is useful in calculations where further operations may be required.
Tips
- Not simplifying the square root terms correctly. Always remember to simplify each factor under the root carefully.
- Forgetting to cancel common factors in the numerator and denominator. Be sure to simplify whenever possible.
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