Question

1)√ав(√а+√в) 2)(√m-√n)√mn 3)(√x+√y)(2√x+√y) 4)(√a-√b)(3√+2√b)

Answer 1

1)√ab(√a+√b)=(√a×√b)(√a+√b)=a√b+b√a; 2)(√m-√n)×√mn=(√m-√n)(√m×√n)=m√n-n√m; 3)(√x+√y)(2√x+√y)=2x+√xy+2√xy+y=2x+3√xy+y; 4)(√a-√b)(3√a+2√b)=3a+2√ab-3√ab-2b=3a-√ab-2b.

Answer 2

Let's simplify each of the expressions:

1. √(a(√a+√b)): To simplify this expression, we can distribute the square root symbol: √(a) * √(√a+√b) Taking the square root of a square root (√(√a)) simplifies to √a. Therefore, the expression becomes: √a * √a+√b √a * √a + √a * √b a + √ab

2. (√m-√n)√mn: We'll simplify this expression using the distributive property: √mn * √m - √mn * √n Taking the square root of mn (√mn) simplifies to √(mn) = √m√n. Therefore, the expression becomes: √m√n * √m - √m√n * √n √m * √m√n - √n * √m√n √m^2√n - √n^2√m m√n - n√m

3. (√x+√y)(2√x+√y): To simplify this expression, we'll use the distributive property: (√x * 2√x) + (√x * √y) + (√y * 2√x) + (√y * √y) Simplifying each term: 2x + √xy + √xy + y Combining like terms: 2x + 2√xy + y

4. (√a-√b)(3√a+2√b): Again, we'll use the distributive property to simplify: (√a * 3√a) + (√a * 2√b) + (-√b * 3√a) + (-√b * 2√b) Simplifying each term: 3a + 2√ab - 3√ab - 2b Combining like terms: 3a - b

So, the simplified forms of the given expressions are:

1. a + √ab
2. m√n - n√m
3. 2x + 2√xy + y
4. 3a - b