find the value of 3 root 12/3 root 3
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Work out the value of (√12 + √3) squared. Assume square roots are positive.
(√12 + √3) squared is just (√12 + √3) mulitipled by itself, so we can rewrite this as
(√12 + √3)*(√12 + √3)
Now we expandthe brackets.
We can mulitply out the brackets using the FOIL method. (First Outside Inside Last)
We multiply the First terms together. The first term in both brackets in this case is √12. The square root of 12 multiplied by the square root of 12 is simply 12.
Now we multiply the Outside terms together. These are the first term in the first bracket and the last term in the last bracket. In this case this is √12 multiplied by √3.
The product property of square roots states that √a multiplied by √b is equal to √(ab). So, √12 multiplied by √3 is equal to √(12 *3) which is √36. The square root of 36 is equal to 6 (for this question we can assume the positive value for square roots).
Now we mulitply the Inside terms together. These are the last term in the first bracket and the first term in the last bracket. In this case this is √3 multiplied by √12. This is the same as the previous step, again giving us a value of 6.
Then we multiply the Last terms together. The last term in both brackets in this case is √3. The square root of 3 multiplied by the square root of 3 is 3.
Finally, we add up all of the values we calculated above.
12 + 6 + 6 + 3
= 27
So our answer is 27.
Remember: If we had subtraction within either of the brackets then we would have to be careful with signs, as we could end up with negative numbers, so would have to be remember to include any minus signs when adding final terms.
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