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2 answers:
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The given three numbers are 5,8,24.
We have to use four operations (Adding, Subtracting,multiplication, division, square, square root, cube, cube root) out of these operation to make the result an irrational number.
There are many more examples that you can write.
Keep in mind
1. Sum of Rational and irrational is always irrational.
2. Difference of rational and irrational is always irrational.
As none of the 5,8,24 is a perfect square , nor addition of any two results in a perfect square, so square root of their addition or subtraction or multiplication results in an irrational number.
Similarly ,apart from 8, none of 5,24 is a perfect cube.So if you add or subtract any number from 8 and take their cube root or square root ,results in an irrational number.
Answer:
3. 37°, 37°, and 106°
Step-by-step explanation:
I am doing #3 as shown in the picture.
Isosceles triangle is a triangle with 2 sides same and their opposite angles same. Those angles are congruent and called base angles. The remaining angle is the vertex angle.
We let each of the base angles as "b" and the vertex angle as "v".
Now,
Vertex Angle is 5 less than 3 times one of the base angles, we can write:
We also know that 3 angles in a triangle add up to 180 degrees, so we can write:
v + b + b = 180
v + 2b = 180
(3b - 5) + 2b = 180
We have replaced "v" with the first equation and created an equation in "b". So now we can solve for b:
Now, finding v:
v = 3b - 5
v = 3(37) - 5
v = 106
Thus, the three angles of the triangle are:
37°, 37°, and 106°