Compare size: root 3 - root 2 and root 6 - root 5 (without calculator)

Compare size: root 3 - root 2 and root 6 - root 5 (without calculator)

Root 3-root 2 > root 6-root 5
Because 3 + 5 + 2 * root sign 15 > 6 + 2 + 2 * root sign 12
That is (root 3 + root 5) ^ 2 > (root 6 + root 2) ^ 2
Root 3 + root 5 > root 6 + root 2
So root 3-root 2 > root 6-root 5

Without calculator, compare the size of root 7 + root 5 and root 2 + root 6, and explain the reasons

The square of the former is larger than that of the latter

How to compare the size of [2 + root 5] and [root 3 + root 6] without calculator As the title

Both are squared
Compare the size after the square

Compare the size of 2 minus root 3 and root 5 minus root 4 without using a calculator

(2-√3)*(2+√3)=4-3=1=5-4=(√5-√4)(√5+2)
Because: 2 + √ 3 √ 5 - √ 4

1 + cos80 under radical - 1-cos80 under radical equals?

=√[1＋(2cos²40°－1)－√[1－(1－2sin²40°)]
=√2[cos40°－sin40°]
=2[(√2/2)cos40°－(√2/2)sin40]
=2cos[45°＋40°]
=2cos85°

Find sin 220 ° and COS 280 °+ 3 sin 20 ° cos 80 °

The original formula is sin220 ° and sin210 ° respectively+
3sin20°cos（60°+20°）
=sin220°+1
2（1-cos20°）+
Three
2sin20°cos20°-3
2sin220°，
=1
2（1-cos20°）+
Three
4sin40°-1-cos40°
Four
=1
4-1
2cos20°+1
2（
Three
2sin40°+1
2cos40°）
=1
4-1
2cos20°+1
2sin70°
=1
4．
So the answer is 1
4．

Find sin 220 ° and COS 280 °+ 3 sin 20 ° cos 80 °

The original formula is sin220 ° and sin210 ° respectively+
3sin20°cos（60°+20°）
=sin220°+1
2（1-cos20°）+
Three
2sin20°cos20°-3
2sin220°，
=1
2（1-cos20°）+
Three
4sin40°-1-cos40°
Four
=1
4-1
2cos20°+1
2（
Three
2sin40°+1
2cos40°）
=1
4-1
2cos20°+1
2sin70°
=1
4．
So the answer is 1
4．

Calculation question: root 9 - root (- 2) 2 - root 16

∫ 9 - ∫ (- 2) ∫ 16 = 3 - ∫ 4-4 = 3-2-4 = - 3 happy!

When 2 < a < 8, the absolute value of (2-A) 2 + 8-A under the root sign=

When 2 < a < 8, the absolute value of (2-A) 2 + (8-A) under the root sign = A-2 + 8-A = 6

(cos40+ 3tan10°)=______ .

cos40°(1+
3tan10°)=sin50°(1+
3tan10°)=sin50°(cos10°+
3sin10°)
cos10°=2sin50°sin(30°+10°)
cos10°=2cos40° sin40°
cos10°=sin80°
cos10°=1
So the answer is: 1