Question

What is the simplified form of the expression 4/5√72y^7 - √128y^7 + 5y^3√18y?

a) 4y^3√2y
b) 4/5y^3√2y
c) 8/5y^3√2y
d) 4y^4√2y

Answer 1

To simplify the expression 4/5√72y^7 - √128y^7 + 5y^3√18y, combine the like terms by simplifying each term individually and then combining the coefficients. The simplified form of the expression is 4y^3√2y.

Step-by-step explanation:

To simplify the expression 4/5√72y^7 - √128y^7 + 5y^3√18y, we need to simplify each term individually and then combine like terms.

1. Simplify 4/5√72y^7. The square root of 72 is 6√2, so the expression becomes (4/5) * 6√2 * y^7, which simplifies to (24/5) * y^7√2.
2. Simplify √128y^7. The square root of 128 is 8√2, so the expression becomes 8√2 * y^7, which simplifies to 8y^7√2.
3. Simplify 5y^3√18y. The square root of 18 is 3√2, so the expression becomes 5 * y^3 * 3√2 * y, which simplifies to 15y^4√2.

Combining the simplified terms, we have (24/5) * y^7√2 - 8y^7√2 + 15y^4√2. The like terms have the same radical and variable factors, so we can combine the coefficients: (24/5 - 8 + 15) * y^7√2.

Simplifying further, we have (31/5) * y^7√2. Therefore, the simplified form of the expression is option a) 4y^3√2y.