Remember area and length scale?

Area scale
= 32 : 18
= 16 : 9 (simplest ratio)

Length scale
= square root of area scale
= sqrt 16 : sqrt 9
= 4 : 3

i square root the 32:18 without simplifying it and couldnt get the ans
must we simplify all ratios if possible before square rooting?

Square root 32 : square root 18 still possible, but you won’t be able to navigate the decimals.

Try dividing the larger decimal number by the smaller decimal number. I think you should still get 4/3.

btw why 21cm and 14cm cant be used as the radius tho

I’m pretty sure “21 cm to 14 cm” is an error in the question.

They probably forgot to remove the numbers before editing the question.

I trust the area ones more.

Because simplifying 21 cm to 14 cm is too easy for a Sec 3 standard question.

Square rooting 18 : 32 and writing down each gives you two irrational numbers,

5.65685425...

and

4.24264069...

What you should do if you want the direct answer (this question is short answer so no working needed) is to divide √32 by √18 directly in the calculator.

√32 ÷ √18 = 1.33333...

This is 4/3 in the form of a recurring decimal. The display will be converted to 4/3 or 1⅓ when you press the fraction button on your calculation.


The ratio simply 4 : 3

Alternatively ,


√32 : √18

= √(16 x 2) : √(9 x 2)

= √16√2 : √9√2

= √16 : √9

= 4 : 3