Question

Find all the real square roots of 16/49.
a) ±4/7
b) ±2/7
c) ±4/√7
d) ±2/√7

Answer 1

The real square roots of 16/49 are ±4/7, as both 4/7 and -4/7, when squared, yield 16/49.

Step-by-step explanation:

The real square roots of 16/49 can be found by considering that the square root function is the inverse operation of squaring. That being the case, to find the square roots of 16/49, we look for a number that, when multiplied by itself, gives 16/49.

The square root of 16 is 4, and the square root of 49 is 7, therefore, the square root of 16/49 is 4/7. Since the question asks for all real square roots, we must consider both the positive and negative roots, as both (4/7)*(4/7) and (-4/7)*(-4/7) will yield 16/49.

So the correct answer is ±4/7, option a).