- #1
Quinn Morris
- 14
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Homework Statement
[tex]\frac{5}{\sqrt{7+3\sqrt{x}}}[/tex] = [tex]\sqrt{7 -3\sqrt{x}}[/tex]
Homework Equations
none
The Attempt at a Solution
does this equal 5 = 7 - 3[tex]\sqrt{x}[/tex]
lkh1986 said:5 = sqrt (49 - 9x - 42 sqrt x)
25 = 49 - 9x - 42 sqrt x
24 = 9x + 42 sqrt x
The rest I leave it to you. You just have to square another time.
Quinn Morris said:i cross multiplied, but I'm a little iffy on my FOIL technique when square roots are throw into the mix
Since there isno "c" in the problem, I guess you missed the "x" key!Quinn Morris said:c=8 i think
Check it!epenguin said:x = 8/3 I think.
If 25= 49- 9x, the 9x= 49-25= 24 so x= 24/9= 8/3 as epenguin said. (But you should still check numerically.)HallsofIvy said:Multiplying
[tex]\frac{5}{\sqrt{7+3\sqrt{x}}}= \sqrt{7 -3\sqrt{x}}[/tex]
on both sides by [itex]\sqrt{7+ 3\sqrt{x}}[/itex] gives [itex]5= \sqrt{(7- 3\sqrt{x})(7+ 3\sqrt{x})}= \sqrt{49- 9x}[/itex], because the product inside the squareroot is "sum times difference". Now squaring gives 25= 49- 9x. That should be easy to solve. Don't forget to check your answer- multiplying both sides by something involving x or squaring both sides can introduce "extraneous" solutions.
A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 multiplied by itself equals 25.
To calculate the square root of a number, you can either use a calculator or use long division. The long division method involves finding the largest square number that is less than or equal to the given number and then finding the difference between the given number and the square number. This process is repeated until the desired level of accuracy is achieved.
A perfect square is a number whose square root is a whole number. For example, 25 is a perfect square because its square root is 5. A non-perfect square is a number whose square root is a decimal or irrational number. For example, the square root of 2 is a non-perfect square because it is an irrational number (1.414213...).
Yes, you can have a negative square root. In fact, every positive number has two square roots - one positive and one negative. For example, the square root of 25 is both 5 and -5.
Square roots are used in many real-life situations, such as calculating the side lengths of a square or finding the dimensions of a square room. They are also used in advanced mathematical concepts, such as in the Pythagorean theorem and in calculus.