To write the expression in the form a√7 where a is an integer, we can simplify the square roots of 112, 23, and 7:
B = 2√112 - 3√23 + 3√7
First, simplify the square roots:
√112 = √(16 * 7) = √16 * √7 = 4√7
√23 stays as it is
√7 stays as it is
Now substitute back into the expression:
B = 2(4√7) - 3(√23) + 3(√7)
B = 8√7 - 3√23 + 3√7
B = (8 + 3)√7 - 3√23
B = 11√7 - 3√23
Therefore, B = 11√7 - 3√23, where a = 11 is an integer.
