### Question 1.State the order of the surds given below.i. ii. iii. iv. v. Answer:In , n is called the order of the surd.Therefore,i. In this, the order of surd is 3.ii. In this, the order of surd is 5.iii. In this, the order of surd is 4.iv. In this, the order of surd is 2.v. In this, the order of surd is 3Question 2.State which of the following are surds. Justify.i. ii. iii. iv. v. vi. Answer:Surds are numbers left in root form (√) to express its exact value. It has an infinite number of non-recurring decimals. Therefore, surds are irrational numbers.Therefore,i. It is a surd ∵ it cannot be expressed as a rational number.ii. It is a surd ∵ it cannot be expressed as a rational number.iii. It is a surd ∵ it cannot be expressed as a rational number.iv.√256 = √162 = 16It is not a surd ∵ it is a rational number.v. It is not a surd ∵ it is a rational number.vi. It is a surd ∵ it cannot be expressed as a rational number.Question 3.Classify the given pair of surds into like surds and unlike surds.i. √52, 5√13ii. √68, 5√3iii. 4√18, 7√2iv. 19√12, 6√3v. 5√22, 7√33vi. 5√5, √75Answer:Two or more surds are said to be similar or like surds if they have the same surd-factor.And,Two or more surds are said to be dissimilar or unlike when they are not similar.Therefore,i. √52, 5√13√52 = √(2×2×13) = 2√135√13∵ both surds have same surd-factor i.e., √13.∴ they are like surds.ii. √68, 5√3√68 = √(2×2×17) = 2√175√3∵ both surds have different surd-factors √17 and √3.∴ they are unlike surds.iii. 4√18, 7√24√18 = 4√(2×3×3) = 4×3√2 = 12√27√2∵ both surds have same surd-factor i.e., √2.∴ they are like surds.iv. 19√12, 6√319√12 = 19√(2×2×3) = 19×2√3 = 38√36√3∵ both surds have same surd-factor i.e., √3.∴ they are like surds.v. 5√22, 7√33∵ both surds have different surd-factors √22 and √33.∴ they are unlike surds.vi. 5√5, √755√5√75 = √(5×5×3) = 5√3∵ both surds have different surd-factors √5 and √3.∴ they are unlike surds.Question 4.Simplify the following surds.i. √27ii. √50iii. √250iv. √112v. √168Answer:i.   ii.   iii.   iv.    v.    Question 5.Compare the following pair of surds.i. 7√2, 5√3ii. √247, √274iii. 2√7, √28iv. 5√5, 7√2v. 4√42, 9√2vi. 5√3, 9vii. 7, 2√5Answer:i. 7√2 , 5√3(7√2)2 = 7 × 7 × √2 × √2⇒ (7√2)2 = 49 × 2⇒ (7√2)2 = 98And(5√3)2 = 5 × 5 × √3 × √3⇒ (5√3)2 = 25 × 3⇒ (5√3)2 = 75Clearly,98 > 75∴ 7√2 > 5√3ii. √247, √274(√247)2 = 247And(√274)2 = 274Clearly,247 < 274∴ √247 < √274iii. 2√7, √28(2√7)2 = 2 × 2 × √7 × √7⇒ (2√7)2 = 4 × 7⇒ (2√7)2 = 28And(√28)2 = 28Clearly,28 = 28∴ 2√7 = √28iv. 5√5, 7√2(5√5)2 = 5 × 5 × √5 × √5⇒ (5√5)2 = 25 × 5⇒ (5√5)2 = 125And(7√2)2 = 7 × 7 × √2 × √2⇒ (7√2)2 = 49 × 2⇒ (7√2)2 = 98Clearly,125 = 98∴ 5√5= 7√2v. 4√42, 9√2(4√42)2 = 4 × 4 × √42 × √42⇒ (4√42)2 = 16 × 42⇒ (4√42)2 = 672And(9√2)2 = 9 × 9 × √2 × √2⇒ (9√2)2 = 81 × 2⇒ (9√2)2 = 162Clearly,672 > 162∴ 4√42 > 9√2vi. 5√3, 9(5√3)2 = 5 × 5 × √3 × √3⇒ (5√3)2 = 25 × 3⇒ (5√3)2 = 75And(9)2 = 9 × 9⇒ (9)2 = 81Clearly,75 < 81∴ 5√3 < 9vii. 7, 2√5(2√5)2 = 2 × 2 × √5 × √5⇒ (2√5)2 = 4 × 5⇒ (2√5)2 = 20And(7)2 = 7 × 7⇒ (7)2 = 49Clearly,49 > 20∴ 7 > 2√5Question 6.Simplify.i. 5√3 + 8√3ii. 9√5 – 4√5 + √125iii. 7√48 – √27 – √3iv. Answer:i. 5√3 + 8√35√3 + 8√3 = (5 + 8)√3⇒ 5√3 + 8√3 = 13√3ii. 9√5 – 4√5 + √1259√5 – 4√5 + √125 = 9√5 – 4√5 + √(5 × 5 × 5)⇒ 9√5 – 4√5 + √125 = 9√5 – 4√5 + √(5 × 5 × 5)⇒ 9√5 – 4√5 + √125 = 9√5 – 4√5 + 5√5⇒ 9√5 – 4√5 + √125 = (9 – 4 + 5)√5⇒ 9√5 – 4√5 + √125 = 10√5iii. 7√48 – √27 – √37√48 – √27 – √3 = 7√(2 × 2 × 2 × 2 × 3) – √(3 × 3 × 3) – √3⇒ 7√48 – √27 – √3 = 7×4√3 – 3√3 – √3⇒ 7√48 – √27 – √3 = 28√3 – 3√3 – √3⇒ 7√48 – √27 – √3 = (28 – 3 – 1)√3⇒ 7√48 – √27 – √3 = 24√3iv.    Question 7.Multiply and write the answer in the simplest form.i. 3√12 × √18ii. 3√12 × 7√15iii. 3√8 × √5iv. 5√8 × 2√8Answer:i. 3√12 × √183√12 × √18 = 3√(2 × 2 × 3) × √(2 × 3 × 3)⇒3√12 × √18 = 3 × 2√3 × 3√2⇒ 3√12 × √18 = 6√3 × 3√2⇒ 3√12 × √18 = 18√6ii. 3√12 × 7√153√12 × 7√15 = 3√(2 × 2 × 3) × 7√(3 × 5)⇒3√12 × 7√15 = 3 × 2√3 × 7√(3 × 5)⇒3√12 × 7√15 = 3 × 2 × 7 × √(3 × 3 × 5)⇒3√12 × 7√15 = 3 × 2 × 7 × 3√5⇒ 3√12 × 7√15 = 126√5iii. 3√8 × √53√8 × √5 = 3√(2 × 2 × 2) × √5⇒3√8 × √5 = 3 × 2√2 × √5⇒ 3√8 × √5 = 3 × 2 ×√(2 × 5)⇒ 3√8 × √5 = 6√10iv. 5√8 × 2√85√8 × 2√8 = 5√(2 × 2 × 2) × 2√(2 × 2 × 2)⇒5√8 × 2√8 = 5 × 2√2 × 2 × 2√2⇒ 5√8 × 2√8 = 5 × 2 × 2 × 2 ×√(2 × 2)⇒ 5√8 × 2√8 = 5 × 2 × 2 × 2 × 2⇒ 5√8 × 2√8 = 80Question 8.Divide, and write the answer in simplest form.i. √98 ÷ √2ii. √125 ÷ √50iii. √54 ÷ √27iv. √310 ÷ √5Answer:i. √98 ÷ √2  ⇒√98 ÷ √2 = 7ii. √125 ÷ √50   iii. √54 ÷ √27 ⇒√54 ÷ √27 = √2iv. √310 ÷ √5  ⇒ √310 ÷ √5 = √62Question 9.Rationalize the denominator.i. ii. iii. iv. v. Answer:i. We know that √5 × √5 = 5, ∴ to rationalize the denominator of multiply both numerator and denominator by √5.  ii. We know that √14 × √14 = 14, ∴ to rationalize the denominator of multiply both numerator and denominator by √14.  iii. We know that √7 × √7 = 7, ∴ to rationalize the denominator of multiply both numerator and denominator by √7.  iv. We know that √3 × √3 = 3, ∴ to rationalize the denominator of multiply both numerator and denominator by √3.  v. We know that √3 × √3 = 3, ∴ to rationalize the denominator of multiply both numerator and denominator by √3.  PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

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# 2019 Board Paper Solution

HSC ENGLISH SET A 2019 21st February, 2019

HSC ENGLISH SET B 2019 21st February, 2019

HSC ENGLISH SET C 2019 21st February, 2019

HSC ENGLISH SET D 2019 21st February, 2019

SECRETARIAL PRACTICE (S.P) 2019 25th February, 2019

HSC XII PHYSICS 2019 25th February, 2019

CHEMISTRY XII HSC SOLUTION 27th, February, 2019

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HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019

HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019

SSC ENGLISH STD 10 5TH MARCH, 2019.

HSC XII ACCOUNTS 2019 6th March, 2019

HSC XII BIOLOGY 2019 6TH March, 2019

HSC XII ECONOMICS 9Th March 2019

SSC Maths I March 2019 Solution 10th Standard11th, March, 2019

SSC MATHS II MARCH 2019 SOLUTION 10TH STD.13th March, 2019

SSC SCIENCE I MARCH 2019 SOLUTION 10TH STD. 15th March, 2019.

SSC SCIENCE II MARCH 2019 SOLUTION 10TH STD. 18th March, 2019.

SSC SOCIAL SCIENCE I MARCH 2019 SOLUTION20th March, 2019

SSC SOCIAL SCIENCE II MARCH 2019 SOLUTION, 22nd March, 2019

XII CBSE - BOARD - MARCH - 2019 ENGLISH - QP + SOLUTIONS, 2nd March, 2019

# HSCMaharashtraBoardPapers2020

(Std 12th English Medium)

HSC ECONOMICS MARCH 2020

HSC OCM MARCH 2020

HSC ACCOUNTS MARCH 2020

HSC S.P. MARCH 2020

HSC ENGLISH MARCH 2020

HSC HINDI MARCH 2020

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# SSCMaharashtraBoardPapers2020

(Std 10th English Medium)

English MARCH 2020

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Hindi (Composite) MARCH 2020

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Mathematics (Paper 1) MARCH 2020

Mathematics (Paper 2) MARCH 2020

Sanskrit MARCH 2020

Sanskrit (Composite) MARCH 2020

Science (Paper 1) MARCH 2020

Science (Paper 2)

Geography Model Set 1 2020-2021

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