What Is The Square Root Of 50 In Simplified Radical Class 8 Maths CBSE

CoursesCourses for KidsFree study materialOffline CentresMoreStore

Talk to our experts

1800-120-456-456

Sign In

• Question Answer

• Class 8

• Maths

• What is the square root of 50 ...

AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsWhat is the square root of 50 in simplified radical form?AnswerVerified545.1k+ viewsHint: To find the simplified radical form of square root of 50, first we will write it as a product of its prime factors. Now, if there will be the same prime factors more than once then we will write it in the exponential form and use the property of exponents ${{\left( {{a}^{m}} \right)}^{n}}={{a}^{m\times n}}$ to simplify the radical expression. The prime factors which may not be paired will be left inside the radical sign.Complete step by step solution:Here we have been asked to write the simplest radical form of square root of 50. Let us assume this expression as E. So we have the radical expression,$\Rightarrow E=\sqrt{50}$Now to simplify the above expression further we need to write it as the product of its prime factors. Since we have the under root sign in the radical expression so we will try to form pairs of two similar prime factors if they will appear and we will use the formula ${{\left( {{a}^{m}} \right)}^{n}}={{a}^{m\times n}}$ to remove them from the radical sign. The factors which will appear only once will be left inside the radical sign. So we can write,\[\Rightarrow 50=2\times 5\times 5\]Factor 5 is appearing twice so in exponential form we can write it as:\[\Rightarrow 50=2\times {{5}^{2}}\]Therefore the expression E becomes:\[\begin{align} & \Rightarrow E=\sqrt{2\times {{5}^{2}}} \\ & \Rightarrow E=\sqrt{2}\times \sqrt{{{5}^{2}}} \\ & \Rightarrow E=\sqrt{2}\times {{\left( {{5}^{2}} \right)}^{\dfrac{1}{2}}} \\ \end{align}\]Using the formula ${{\left( {{a}^{m}} \right)}^{n}}={{a}^{m\times n}}$ we get,\[\begin{align} & \Rightarrow E=\sqrt{2}\times {{5}^{2\times \dfrac{1}{2}}} \\ & \Rightarrow E=\sqrt{2}\times 5 \\ & \therefore E=5\sqrt{2} \\ \end{align}\]Hence, $5\sqrt{2}$ is the simplified radical form of $\sqrt{50}$.Note: Do not substitute the value of $\sqrt{2}=1.414$ in the obtained expression to find the product because we haven’t been asked to find the square root but we just have to simplify the expression. You must remember the formulas of exponents as they are used to simplify the radical expressions.Recently Updated PagesBasicity of sulphurous acid and sulphuric acid areMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 11 Economics: Engaging Questions & Answers for SuccessMaster Class 12 English: Engaging Questions & Answers for SuccessMaster Class 12 Social Science: Engaging Questions & Answers for SuccessBasicity of sulphurous acid and sulphuric acid areMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 11 Economics: Engaging Questions & Answers for SuccessMaster Class 12 English: Engaging Questions & Answers for SuccessMaster Class 12 Social Science: Engaging Questions & Answers for Success

• 1
• 2

Trending doubtsName the states through which the Tropic of Cancer class 8 social science CBSEWhat are the 12 elements of nature class 8 chemistry CBSEIn Indian rupees 1 trillion is equal to how many c class 8 maths CBSEWho created the image of Bharat Mata for the first class 8 social science CBSEWhat is the Balkan issue in brief class 8 social science CBSEDescribe the elements of Belgian model for accommodating class 8 social science CBSEName the states through which the Tropic of Cancer class 8 social science CBSEWhat are the 12 elements of nature class 8 chemistry CBSEIn Indian rupees 1 trillion is equal to how many c class 8 maths CBSEWho created the image of Bharat Mata for the first class 8 social science CBSEWhat is the Balkan issue in brief class 8 social science CBSEDescribe the elements of Belgian model for accommodating class 8 social science CBSE

• 1
• 2