Add and subtract. Assume that all variables represent positive real numbers.

Ask by Davison Tyler. in the United States

Mar 26,2025

Question

Add and subtract. Assume that all variables represent positive real numbers. $$ \sqrt{9 b^{3}}+\sqrt{25 b^{3}}-\sqrt{16 b^{3}} $$

UpStudy AI · Accepted Answer

1. Write each radical as the product of the square roots:
   $$
   \sqrt{9b^3} = \sqrt{9} \cdot \sqrt{b^3}, \quad \sqrt{25b^3} = \sqrt{25} \cdot \sqrt{b^3}, \quad \sqrt{16b^3} = \sqrt{16} \cdot \sqrt{b^3}.
   $$

2. Evaluate the numerical square roots:
   $$
   \sqrt{9} = 3, \quad \sqrt{25} = 5, \quad \sqrt{16} = 4.
   $$

3. Express each term:
   $$
   \sqrt{9b^3} = 3\sqrt{b^3}, \quad \sqrt{25b^3} = 5\sqrt{b^3}, \quad \sqrt{16b^3} = 4\sqrt{b^3}.
   $$

4. Simplify $$\sqrt{b^3}$$ by factoring the exponent:
   $$
   \sqrt{b^3} = \sqrt{b^2 \cdot b} = \sqrt{b^2} \sqrt{b} = b\sqrt{b}.
   $$

5. Substitute back into the expression:
   $$
   \sqrt{9b^3} + \sqrt{25b^3} - \sqrt{16b^3} = 3b\sqrt{b} + 5b\sqrt{b} - 4b\sqrt{b}.
   $$

6. Combine like terms:
   $$
   (3+5-4)b\sqrt{b} = 4b\sqrt{b}.
   $$

Thus, the final simplified expression is:
$$
4b\sqrt{b}.
$$
The simplified expression is $$4b\sqrt{b}$$.

Add and subtract. Assume that all variables represent positive real numbers.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions