It's been a few years since I've done algebra, and many more since we've been expected to do it without a calculator like the GMAT rules state. Please help me figure out these two problems without the use of a calculator.
1.
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√(16)(20) + (8)(32) = The answer is -4
2.
1
---------
0.75 - 1
The answer is 24
I don't know how to get these answers. Please help. Thank you.
I have a problem getting your answers two. They have probably been interchanged inadvertently.
1.
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√(16)(20) + (8)(32)
=√(64*5+64*4)
=√(64*(5+4))
=8√(9)
=8*3
=24
2.
1
---------
0.75 - 1
=1/(0.75-1)
=1/(-0.25)
=-1/(1/4)
=-4/1
=-4
Thank you, my mistake on mixing up the answers when typing. I get number two now. But on number one, how do you get to
=√(64*5+64*4)
and then do you combine 64s for
=√(64*(5+4))
thank you so much
I break down 16*20 into its prime factors, or 64*5 to find if the other term has similar factors.
I did find a common factor of 64 by changing 8*32 to 4*64.
The rest you know.
Sure, I'd be happy to help you solve these algebraic equations without using a calculator.
1. Let's tackle the first equation:
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√(16)(20) + (8)(32) = -4
To simplify the equation, we need to perform the calculations inside the square root and the addition separately.
Inside the square root:
√(16)(20) = √320
We can simplify this further by factoring out perfect squares from inside the square root:
√320 = √(16 × 20) = √16 × √20 = 4√20
Now, let's focus on the addition:
(8)(32) = 256
Now, let's substitute these simplified values back into the original equation:
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4√20 + 256 = -4
To isolate the square root term, subtract 256 from both sides:
4√20 = -260
Divide both sides by 4 to solve for √20:
√20 = -65
This result is not possible since square roots are always positive. Therefore, there must be an error in the given equation or solution.
2. Now, let's move on to the second equation:
1
------
0.75 - 1
We need to simplify the expression on the bottom first, and then divide 1 by that result.
Subtracting the fractions:
0.75 - 1 = -0.25
Now we have:
1
------
-0.25
To divide by a fraction, we invert the divisor and multiply:
1 × (-4/1) = -4
Therefore, the value of the expression is -4.