Question

5. Sarahi found the distance between two points on a coordinate plane to be √74. Can this answer be simplified? Explain.

Answer 1

Answer:

The answer can't be simplified.

Step-by-step explanation:

In order to answer the question, you have to calculate the prime factors of 74 to see if the expression can be simplified.

If at least one of the prime factors has an exponent bigger or equal than 2 (because the expression has a squareroot), then the expression can be simplified using the properties of exponential numbers and irrational numbers to extract the factor or the factors from the squareroot.

(For example the property $\sqrt[n]{x^{k+n} } =\sqrt[n]{(x^{k})(x^{n})}=x\sqrt[n]{x^{k} }$)

Calculating the prime factors:

74/2 = 37 but 37 is a prime number so:

37/37 =1

74 = 2 x 37

Therefore, $\sqrt{74}$ can't be expressed as a simplier number.