Question

Evaluate √10 x √5
​ AND
Factorise y^4 - 16

Answer 1

the answer to your questions is this pic above

Answer 2

Evaluate √10 x √5 = 5√2

Factorize y⁴ - 16 = (y²-4)(y²+4)

Explanation:

Given Equation:

1. Evaluate √10 x √5

2. Factorise y^4 - 16

Evaluate:

1. √10 × √5

==> We can split the √10 into √5×√2

==> √5 ×√2 × √5

==> We know that √5 × √5 = 5

==> 5 × √2

Evaluate √10 x √5 = 5√2

Factorise:

2. y⁴ - 16

==> we know that 16 is a square of 4

==>  y⁴ - 4²

==> (y²)²-4²

a²-b² = (a+b)(a-b)

==> a = y²

==> b = 4

Substitute the values in this equation a²-b² = (a+b)(a-b)

==> (y²)²-4² = (y²-4)(y²+4)

Factorize y⁴ - 16 = (y²-4)(y²+4)