multiply and simplify by factoring
sqrt20a^11b*sqrt8a^12b^11
To multiply and simplify the expression: √20a^11b * √8a^12b^11 by factoring, follow these steps:
Step 1: Separate the factors inside each square root.
√(20 * a^11 * b) * √(8 * a^12 * b^11)
Step 2: Simplify the numbers under the square roots by factoring out perfect squares.
√(4 * 5 * a^10 * a * b) * √(4 * 2 * a^10 * a^2 * b^10 * b)
Step 3: Simplify each square root separately.
√(4 * 5 * a^10) * √(4 * 2 * a^10 * b^10 * a * b)
Step 4: Further simplify the numbers under the square roots.
2 * √(5 * a^10) * 2 * √(2 * a^10 * b^10 * a * b)
Step 5: Combine like terms inside each square root.
4 * √(10 * a^10) * √(2 * a^10 * b^10 * a * b)
Step 6: Multiply the coefficients outside the square roots.
4 * 2 * √(10 * a^10) * √(2 * a^10 * b^10 * a * b)
Step 7: Simplify the numbers outside the square roots.
8√(10 * a^10) * √(2 * a^10 * b^10 * a * b)
Step 8: Combine the square root terms.
8√((10 * a^10) * (2 * a^10 * b^10 * a * b))
Step 9: Multiply the terms inside the square root.
8√(20 * a^20 * b^10 * a^2 * b)
Step 10: Simplify the square root by grouping like terms.
8 * (a^10 * b^5) * √(20 * a^2)
Step 11: The final simplified expression is:
8a^10b^5√(20a^2)