Answer:
The smallest value of p+q is 11
It happens when p = 6 and q = 5.
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Explanation:
Let's factor 180 in such a way that exactly one factor is a perfect square.
I'll ignore the trivial factor of 1.
Here are the possible factorizations we could go with:
180 = 4*45
180 = 9*20
180 = 36*5
Those factorizations then lead to the following
Then we have
p+q = 2+45 = 47
p+q = 3+20 = 23
p+q = 6+5 = 11
The smallest value of p+q is 11 and it happens when p = 6 and q = 5.
Side note: p+q is smallest when we go with the largest perfect square factor.
Rational numbers are basically numbers which are in the form of p/q where p and q are not equal to 0
Therefore p can be both +ve and -ve
But Natural numbers start from 1 , ie they are always positive
Therefore the answer is
B. sometimes
Left one i think thats the one
The volume of the box will be equal to V= 288 cubic inches.
<h3>What is volume?</h3>
Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the Cuboid.
The given parameters of the box are:-
12 inches long
6 inches wide
4 inches tall
So the volume of the box will be:-
V = L x W x H
V = 12 x 6 x 4
V = 288 square inches
Therefore the volume of the box will be equal to V= 288 cubic inches.
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