Answer:
4√2 × 4√8 = 64, an integer.
Step-by-step explanation:
a) 4√2 × 4√8
First let's remember that a square root can be rewritten as a 1/2 exponent,
Therefore the expression we have can be rewritten as
[tex]4(2^{1/2} )4(8^{1/2})[/tex]
We are going to write all numbers in their prime factor expressions:
*Note: Remember that when we multiply two numbers with the same base but different exponents we sum up the exponents*
*Also, when we elevate one exponent to another exponent, we multiply the exponents*
[tex]4(2^{1/2} )4(8^{1/2})\\=2^2 (2^{1/2})2^2 (2^{3})^{1/2} \\ =2^2 (2^{1/2})2^2 (2^{3/2})\\=2^22^2(2^{1/2}2^{3/2})\\=16(2^{4/2})\\=16(2^2)\\=16(4)\\=64[/tex]
Therefore, the expression 4√2 × 4√8 = 64 and therefore is an integer
