1:x = x:64. What One Number Can Replace x?

Given Proportion

If 1:x = x:64

So we need to find one number x.

Rewrite this Proportion to Simplify

we can write it as

1/x = x/64

Cross multiply the numerators and denominators.

From the left-hand side, denominator move the x to right-hand side numerator and multiply with existing right-hand side numerator x

From right-hand side denominator move 64 to left-hand side numerator and multiply with existing left-hand side numerator 1

Now it becomes, 1 X 64 = x X x

Where 'X' represents multiplication

Simplification

Simplify further 64 = x^2

If you multiply x with another x, it will become x power 2 which we can write it as x^2

Solution

Lets write as x^2 = 64

we can write 64 as 8^2 because 8 power 2 will be 64

x^2 = 8^2

✅ x=8

👉 So the value of x is 8