sqrt(a)* sqrt(b)To verify if its value is 6sqrt(5) when a= 18 and b= 10, let's substitute the given values for a and b. Then we will simplify the expression.
As we can see, the value of the expression for the given values of a and b is indeed 6sqrt(5).
b Now we want to find two other pairs of positive integers a and b that make the given equation true. Let's use the fact that 6sqrt(5) can be rewritten as sqrt(180) — as shown in Part A.
6sqrt(5)= sqrt(180)
By the Multiplication Property of Square Roots, the product of two squares is equal to the square root of the product of the radicands.
sqrt(a)* sqrt(b)= sqrt(ab)
Therefore, we want to find values a and b that satisfy the following equation.
sqrt(ab)&= sqrt(180)
& ⇓
ab&=180
To find the possible values of a and b, we will split 180 into factor pairs.
180&=18* 10
&=20* 9
&=30* 6
&=36* 5
&=45* 4
&=60* 3
&=90* 2
The square root of any of these products is equal to 6sqrt(5). Hence, two possible pairs of values for a and b are as follows.
la=4 b=45 and la=3 b=60
Note that the values of a and b can be reversed within any pair.
